Simple factoring
•Download as PPT, PDF•
0 likes•319 views
The document discusses factoring polynomials by finding the greatest common factor (GCF) and using the distributive property. It provides examples of finding the GCF, using the distributive property to factor expressions, and factoring polynomials. Practice problems are given to factor expressions using these techniques.
Report
Share
Report
Share
![Greatest common factor (GCF) ,[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
March 17, 2015
Today's class will include a warm-up, factoring polynomials using the greatest common factor (GCF) method and factoring by grouping, and Khan Academy assignments due tonight. Students should show all their work to receive credit for class work involving factoring polynomials using GCF and grouping methods.
6.3 gcf factoring
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of finding the GCF of numbers and terms with variables. The key steps are to find the GCF, then divide each term by the GCF to obtain factors in parentheses. Examples show factoring various polynomials using this method. The objective is for students to learn to factor polynomials by using the GCF to find the common factors.
Functions - Domain and Range
This question involves both combinatorics and functions. We need to find the domain of the given combination using basic principles of functions.
Algebra 2 Section 0-2
The FOIL method is used to multiply binomials. It involves multiplying the First, Outer, Inner, and Last terms. Examples show using FOIL to multiply terms like (x - 3)(x + 6), finding the x2, x, x, and constant terms. The area of a square garden that is expanded by 4 feet in length and 6 feet in width can be found by treating the original length as x, and using the expressions (x + 4) for the new length and (x + 6) for the new width.
Algebra 2 Section 0-3
Here are some key patterns to look for when factoring quadratics:
- Factor out the greatest common factor (GCF)
- Use the difference of squares pattern for expressions of the form a2 - b2
- Use the perfect square trinomial pattern for expressions of the form (a + b)2
- For general quadratics, multiply the first and last terms, find factors that sum to the middle term, and group terms
- Be on the lookout for factoring out expressions like (x - a) from each term
Understanding these common patterns is essential for successfully factoring quadratic expressions. Looking for these patterns can help reveal the underlying structure needed to factor the expression.
Algebraic expressions
Polynomials are algebraic expressions involving variables and their powers. The degree of a polynomial is the highest power of the variable. To add or subtract polynomials, like terms must be combined. To multiply polynomials, the distributive property and FOIL method are used. Special formulas exist for multiplying the sum and difference of expressions.
Expresiones algebraicas
The document defines algebraic expressions and provides examples of basic operations - addition, subtraction, multiplication, and division - that can be performed on algebraic expressions. It also covers evaluating algebraic expressions for given variable values and important algebraic identities called "notable products", including differences and sums of squares and cubes. Examples are given for each type of operation and identity.
Alg2 lesson 5-4
This document provides instructions for factoring polynomials. It discusses finding the greatest common factor of terms, factoring expressions using the difference of squares and sum/difference of cubes formulas, and factoring the numerator and denominator when simplifying fractions.
Recommended
March 17, 2015
Today's class will include a warm-up, factoring polynomials using the greatest common factor (GCF) method and factoring by grouping, and Khan Academy assignments due tonight. Students should show all their work to receive credit for class work involving factoring polynomials using GCF and grouping methods.
6.3 gcf factoring
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of finding the GCF of numbers and terms with variables. The key steps are to find the GCF, then divide each term by the GCF to obtain factors in parentheses. Examples show factoring various polynomials using this method. The objective is for students to learn to factor polynomials by using the GCF to find the common factors.
Functions - Domain and Range
This question involves both combinatorics and functions. We need to find the domain of the given combination using basic principles of functions.
Algebra 2 Section 0-2
The FOIL method is used to multiply binomials. It involves multiplying the First, Outer, Inner, and Last terms. Examples show using FOIL to multiply terms like (x - 3)(x + 6), finding the x2, x, x, and constant terms. The area of a square garden that is expanded by 4 feet in length and 6 feet in width can be found by treating the original length as x, and using the expressions (x + 4) for the new length and (x + 6) for the new width.
Algebra 2 Section 0-3
Here are some key patterns to look for when factoring quadratics:
- Factor out the greatest common factor (GCF)
- Use the difference of squares pattern for expressions of the form a2 - b2
- Use the perfect square trinomial pattern for expressions of the form (a + b)2
- For general quadratics, multiply the first and last terms, find factors that sum to the middle term, and group terms
- Be on the lookout for factoring out expressions like (x - a) from each term
Understanding these common patterns is essential for successfully factoring quadratic expressions. Looking for these patterns can help reveal the underlying structure needed to factor the expression.
Algebraic expressions
Polynomials are algebraic expressions involving variables and their powers. The degree of a polynomial is the highest power of the variable. To add or subtract polynomials, like terms must be combined. To multiply polynomials, the distributive property and FOIL method are used. Special formulas exist for multiplying the sum and difference of expressions.
Expresiones algebraicas
The document defines algebraic expressions and provides examples of basic operations - addition, subtraction, multiplication, and division - that can be performed on algebraic expressions. It also covers evaluating algebraic expressions for given variable values and important algebraic identities called "notable products", including differences and sums of squares and cubes. Examples are given for each type of operation and identity.
Alg2 lesson 5-4
This document provides instructions for factoring polynomials. It discusses finding the greatest common factor of terms, factoring expressions using the difference of squares and sum/difference of cubes formulas, and factoring the numerator and denominator when simplifying fractions.
3/1/12 Factor by Grouping and Factoring into Quadratic Form
The document discusses factoring polynomials by grouping and factoring polynomials into quadratic form. It provides examples of factoring polynomials using these methods, such as factoring x3 - 3x2 - 16x + 48 as (x - 3)(x2 - 16). Students are asked to complete factoring exercises and solve a challenge problem involving factoring the volume equation of a jewelry box to find its dimensions.
Η έννοια της εξίσωσης, Οι εξισώσεις: α + x = β, x – α = β, α – x = β, αx = β,...
Εξισώσεις και προβλήματα, , Α.4.1, Η έννοια της εξίσωσης, Οι εξισώσεις, α + x = β, x – α = β,
α – x = β, αx = β, α : x = β , x : α = βα , , ΜΑΘΗΜΑΤΙΚΑ Α΄ΓΥΜΝΑΣΙΟΥ, Μέρος Α' , Κεφάλαιο 3ο, Οι φυσικοί αριθμοί, teagher, Εκπαιδευτικό βίντεο από τo ΚΑΛΙΤΣΑ : https://mcjmcjmcj.wordpress.com/
Άρθρο του μαθήματος: https://wp.me/PJcUD-8DN/
#teagher, #ΕΚΠΑΙΔΕΥΣΗ, #ΜΑΘΗΜΑΤΑ, #ΓΥΜΝΑΣΙΟ #ΠΡΩΤΗΓΥΜΝΑΣΙΟΥ, #ΛΥΣΕΙΣ, #ΑΠΑΝΤΗΣΕΙΣ, #ΚΑΛΙΤΣΑ,
Math ppt copy (2)
- An algebraic expression involving variables with only non-negative integer powers is called a polynomial. The highest power of the variable in a polynomial is called its degree.
- Polynomials can be classified by their degree and number of terms. For example, a polynomial of degree 2 with 3 terms is called a trinomial.
- Common algebraic identities involving polynomials include factoring expressions like (a+b)2, (a-b)2, and a2-b2. Polynomials can also be factored using the difference of squares or sum/difference of cubes identities.
125 5.1
The document discusses various techniques for finding antiderivatives (indefinite integrals). It covers:
1) Using the power rule to find antiderivatives by increasing the exponent by 1 and dividing by the new exponent.
2) Rewriting expressions with rational or negative exponents before taking the antiderivative.
3) Expanding expressions, like using FOIL, before taking the antiderivative term by term.
4) Simplifying expressions, like factoring, before taking the antiderivative.
5) Setting up and solving word problems involving antiderivatives to find functions for quantities like profit, distance, and rate of change.
125 11.1
The document discusses various techniques for evaluating indefinite integrals (antiderivatives), including:
1) Using power rules to evaluate basic integrals like ∫ 4x3 dx = x4 + C
2) Expanding rational or negative exponents before integrating
3) Expanding expressions before integrating term by term
4) Simplifying rational expressions by factoring and canceling before integrating
5) Setting up word problems involving integrals to find related functions like total cost, revenue, distance over time.
Algebra presentation on topic modulus function and polynomials
Algebra Presentation on Topic Modulus Function and Polynomials Created by: Chiquita & Tyo
Performance Task Binus School Bekasi
Algebra presentation on topic modulus function and polynomials
Algebra Presentation on Topic Modulus Function and Polynomials Created by Prastyo
Performance Task Binus School Bekasi
1202 ch 12 day 2
The document provides an introduction to evaluating limits, including:
1. The limit of a constant function is the constant.
2. Common limit laws can be used to evaluate limits of sums, differences, products, and quotients if the individual limits exist.
3. Special techniques may be needed to evaluate limits that involve indeterminate forms, such as 0/0, infinity/infinity, or limits approaching infinity. These include factoring, graphing, and rationalizing.
1201 ch 12 day 1
This document contains examples and explanations of limits involving various functions. Some key points covered include:
- Substitution can be used to evaluate limits, such as substituting 2 into -2x^3.
- Left and right hand limits must agree for the overall limit to exist.
- The limit of a piecewise function exists if the left and right limits are the same.
- Graphs can help verify limit calculations and show discontinuities.
- Special limits involving trigonometric and greatest integer functions are evaluated.
mr. amato's class presentation
to satisfy tech. requirement i have demonstrated ability to create, enhance and manipulate a slide presentation
2.1 Revision Game
The document contains 4 math problems: 1) Simplifying a fractional expression involving powers of p, 2) Expanding and simplifying a polynomial expression, 3) Simplifying a fractional expression involving powers of x, 4) Finding the value of p that gives a repeated real root of a quadratic equation.
1203 ch 12 day 3
Here are the problems from the slides with their solutions:
1. Find the slope of the line tangent to the graph of the function f(x) = x^2 - 5x + 8 at the point P(1,4).
Slope = -3
2. Find the equation of the tangent line to the curve f(x) = 2x^2 - 3 at the point P(1,-1) using point-slope form.
y - (-1) = 4(x - 1)
3. Find the equation of the tangent line to the curve f(x) = x + 6 at the point P(3,3) using point-slope form.
y
Algebra
The document contains 6 problems related to algebra and numbers along with their solutions. Problem 1 involves a number guessing game between two players and determining the minimum number of rounds needed. Problem 2 examines properties of a polynomial where the polynomial equals certain values for distinct integer inputs. Problem 3 finds all integer solutions to a system of equations involving cubes of variables. Problem 4 determines the value of a polynomial of degree 8 at a particular input, given its values at other integers. Problems 5 and 6 involve finding the smallest integer greater than an expression and the minimum possible value of a product of variables, respectively, given an equation relating the variables.
Foil
The document provides instructions on using the FOIL method to multiply binomials. It explains that FOIL is an acronym that stands for First, Outer, Inner, Last - representing the terms to multiply when multiplying two binomials. Several examples are worked out step-by-step using the FOIL method, showing the multiplication of the first, outer, inner, and last terms and combining like terms.
Maxima and minima
This document discusses maxima and minima of functions of two independent variables. It provides the definitions of a relative minimum/maximum point as one where the function value at that point is less than or equal to/greater than or equal to the value at neighboring points. It describes stationary points as those where the function is maximum or minimum, and extreme values as the function values at stationary points. A working rule is given to determine maxima and minima, involving taking partial derivatives and checking signs of second-order derivatives. An example finds the maximum of the function f(x,y)=x^2+y^2+6x+12 at the stationary point (-3,0), with maximum value of 3.
Ankit maths ppt
A polynomial is an algebraic expression involving variables and constants that is formed using addition, subtraction, and multiplication, but not division. The degree of a polynomial refers to the highest power of the variable. Polynomials can be classified based on their number of terms as monomials (one term), binomials (two terms), or trinomials (three terms). They can also be classified based on degree as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), or of higher degrees. The number of zeros of a polynomial is equal to its degree.
Bt0063 mathematics for it
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
Polynomials
It's an introduction to polynomials with an explanation of The Remainder Theorem and The Factor Theorem for Class 10 students. It has some questions for the explanation of the concepts
Addsub poly
Adding and subtracting polynomials involves combining like terms. To add or subtract polynomials, identify like terms and combine them. For example, to add 12p^3 + 11p^2 + 8p^3, the like terms 12p^3 and 8p^3 are combined to get 20p^3, and 11p^2 is left unchanged. Polynomials can be added or subtracted either vertically by aligning like terms or horizontally by regrouping terms. The process is similar to adding and subtracting numbers.
Limits
This document discusses limits of functions. It begins by defining the limit of a function f(x) as x approaches a number c as the value that f(x) approaches as x gets closer to c. It provides examples of limits, including one-sided limits and limits at infinity. Key theorems are presented for computing limits, including properties of limits and the sandwich theorem. The document focuses on conceptual understanding and applying techniques to evaluate a variety of limit examples.
4.2 notes
Graph linear equations in a coordinate plane by following these steps:
1) Choose a domain of at least three convenient values for the variable.
2) Solve the linear equation for those values to obtain ordered pairs.
3) Plot the ordered pairs on a coordinate plane to graph the line represented by the linear equation. Vertical lines must pass through only one point for the graph to represent a function.
4.4 notes
The document discusses slope and how it represents the rate of change of a line. It defines slope as the rise over the run between two points on a line. Positive slope lines rise from left to right, negative slope lines rise from right to left, horizontal lines have zero slope, and vertical lines have undefined slope. The slope formula is defined as the change in y over the change in x between two points.
More Related Content
What's hot
3/1/12 Factor by Grouping and Factoring into Quadratic Form
The document discusses factoring polynomials by grouping and factoring polynomials into quadratic form. It provides examples of factoring polynomials using these methods, such as factoring x3 - 3x2 - 16x + 48 as (x - 3)(x2 - 16). Students are asked to complete factoring exercises and solve a challenge problem involving factoring the volume equation of a jewelry box to find its dimensions.
Η έννοια της εξίσωσης, Οι εξισώσεις: α + x = β, x – α = β, α – x = β, αx = β,...
Εξισώσεις και προβλήματα, , Α.4.1, Η έννοια της εξίσωσης, Οι εξισώσεις, α + x = β, x – α = β,
α – x = β, αx = β, α : x = β , x : α = βα , , ΜΑΘΗΜΑΤΙΚΑ Α΄ΓΥΜΝΑΣΙΟΥ, Μέρος Α' , Κεφάλαιο 3ο, Οι φυσικοί αριθμοί, teagher, Εκπαιδευτικό βίντεο από τo ΚΑΛΙΤΣΑ : https://mcjmcjmcj.wordpress.com/
Άρθρο του μαθήματος: https://wp.me/PJcUD-8DN/
#teagher, #ΕΚΠΑΙΔΕΥΣΗ, #ΜΑΘΗΜΑΤΑ, #ΓΥΜΝΑΣΙΟ #ΠΡΩΤΗΓΥΜΝΑΣΙΟΥ, #ΛΥΣΕΙΣ, #ΑΠΑΝΤΗΣΕΙΣ, #ΚΑΛΙΤΣΑ,
Math ppt copy (2)
- An algebraic expression involving variables with only non-negative integer powers is called a polynomial. The highest power of the variable in a polynomial is called its degree.
- Polynomials can be classified by their degree and number of terms. For example, a polynomial of degree 2 with 3 terms is called a trinomial.
- Common algebraic identities involving polynomials include factoring expressions like (a+b)2, (a-b)2, and a2-b2. Polynomials can also be factored using the difference of squares or sum/difference of cubes identities.
125 5.1
The document discusses various techniques for finding antiderivatives (indefinite integrals). It covers:
1) Using the power rule to find antiderivatives by increasing the exponent by 1 and dividing by the new exponent.
2) Rewriting expressions with rational or negative exponents before taking the antiderivative.
3) Expanding expressions, like using FOIL, before taking the antiderivative term by term.
4) Simplifying expressions, like factoring, before taking the antiderivative.
5) Setting up and solving word problems involving antiderivatives to find functions for quantities like profit, distance, and rate of change.
125 11.1
The document discusses various techniques for evaluating indefinite integrals (antiderivatives), including:
1) Using power rules to evaluate basic integrals like ∫ 4x3 dx = x4 + C
2) Expanding rational or negative exponents before integrating
3) Expanding expressions before integrating term by term
4) Simplifying rational expressions by factoring and canceling before integrating
5) Setting up word problems involving integrals to find related functions like total cost, revenue, distance over time.
Algebra presentation on topic modulus function and polynomials
Algebra Presentation on Topic Modulus Function and Polynomials Created by: Chiquita & Tyo
Performance Task Binus School Bekasi
Algebra presentation on topic modulus function and polynomials
Algebra Presentation on Topic Modulus Function and Polynomials Created by Prastyo
Performance Task Binus School Bekasi
1202 ch 12 day 2
The document provides an introduction to evaluating limits, including:
1. The limit of a constant function is the constant.
2. Common limit laws can be used to evaluate limits of sums, differences, products, and quotients if the individual limits exist.
3. Special techniques may be needed to evaluate limits that involve indeterminate forms, such as 0/0, infinity/infinity, or limits approaching infinity. These include factoring, graphing, and rationalizing.
1201 ch 12 day 1
This document contains examples and explanations of limits involving various functions. Some key points covered include:
- Substitution can be used to evaluate limits, such as substituting 2 into -2x^3.
- Left and right hand limits must agree for the overall limit to exist.
- The limit of a piecewise function exists if the left and right limits are the same.
- Graphs can help verify limit calculations and show discontinuities.
- Special limits involving trigonometric and greatest integer functions are evaluated.
mr. amato's class presentation
to satisfy tech. requirement i have demonstrated ability to create, enhance and manipulate a slide presentation
2.1 Revision Game
The document contains 4 math problems: 1) Simplifying a fractional expression involving powers of p, 2) Expanding and simplifying a polynomial expression, 3) Simplifying a fractional expression involving powers of x, 4) Finding the value of p that gives a repeated real root of a quadratic equation.
1203 ch 12 day 3
Here are the problems from the slides with their solutions:
1. Find the slope of the line tangent to the graph of the function f(x) = x^2 - 5x + 8 at the point P(1,4).
Slope = -3
2. Find the equation of the tangent line to the curve f(x) = 2x^2 - 3 at the point P(1,-1) using point-slope form.
y - (-1) = 4(x - 1)
3. Find the equation of the tangent line to the curve f(x) = x + 6 at the point P(3,3) using point-slope form.
y
Algebra
The document contains 6 problems related to algebra and numbers along with their solutions. Problem 1 involves a number guessing game between two players and determining the minimum number of rounds needed. Problem 2 examines properties of a polynomial where the polynomial equals certain values for distinct integer inputs. Problem 3 finds all integer solutions to a system of equations involving cubes of variables. Problem 4 determines the value of a polynomial of degree 8 at a particular input, given its values at other integers. Problems 5 and 6 involve finding the smallest integer greater than an expression and the minimum possible value of a product of variables, respectively, given an equation relating the variables.
Foil
The document provides instructions on using the FOIL method to multiply binomials. It explains that FOIL is an acronym that stands for First, Outer, Inner, Last - representing the terms to multiply when multiplying two binomials. Several examples are worked out step-by-step using the FOIL method, showing the multiplication of the first, outer, inner, and last terms and combining like terms.
Maxima and minima
This document discusses maxima and minima of functions of two independent variables. It provides the definitions of a relative minimum/maximum point as one where the function value at that point is less than or equal to/greater than or equal to the value at neighboring points. It describes stationary points as those where the function is maximum or minimum, and extreme values as the function values at stationary points. A working rule is given to determine maxima and minima, involving taking partial derivatives and checking signs of second-order derivatives. An example finds the maximum of the function f(x,y)=x^2+y^2+6x+12 at the stationary point (-3,0), with maximum value of 3.
Ankit maths ppt
A polynomial is an algebraic expression involving variables and constants that is formed using addition, subtraction, and multiplication, but not division. The degree of a polynomial refers to the highest power of the variable. Polynomials can be classified based on their number of terms as monomials (one term), binomials (two terms), or trinomials (three terms). They can also be classified based on degree as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), or of higher degrees. The number of zeros of a polynomial is equal to its degree.
Bt0063 mathematics for it
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
Polynomials
It's an introduction to polynomials with an explanation of The Remainder Theorem and The Factor Theorem for Class 10 students. It has some questions for the explanation of the concepts
Addsub poly
Adding and subtracting polynomials involves combining like terms. To add or subtract polynomials, identify like terms and combine them. For example, to add 12p^3 + 11p^2 + 8p^3, the like terms 12p^3 and 8p^3 are combined to get 20p^3, and 11p^2 is left unchanged. Polynomials can be added or subtracted either vertically by aligning like terms or horizontally by regrouping terms. The process is similar to adding and subtracting numbers.
Limits
This document discusses limits of functions. It begins by defining the limit of a function f(x) as x approaches a number c as the value that f(x) approaches as x gets closer to c. It provides examples of limits, including one-sided limits and limits at infinity. Key theorems are presented for computing limits, including properties of limits and the sandwich theorem. The document focuses on conceptual understanding and applying techniques to evaluate a variety of limit examples.
What's hot (20)
3/1/12 Factor by Grouping and Factoring into Quadratic Form
3/1/12 Factor by Grouping and Factoring into Quadratic Form
Η έννοια της εξίσωσης, Οι εξισώσεις: α + x = β, x – α = β, α – x = β, αx = β,...
Η έννοια της εξίσωσης, Οι εξισώσεις: α + x = β, x – α = β, α – x = β, αx = β,...
Algebra presentation on topic modulus function and polynomials
Algebra presentation on topic modulus function and polynomials
Algebra presentation on topic modulus function and polynomials
Algebra presentation on topic modulus function and polynomials
Viewers also liked
4.2 notes
Graph linear equations in a coordinate plane by following these steps:
1) Choose a domain of at least three convenient values for the variable.
2) Solve the linear equation for those values to obtain ordered pairs.
3) Plot the ordered pairs on a coordinate plane to graph the line represented by the linear equation. Vertical lines must pass through only one point for the graph to represent a function.
4.4 notes
The document discusses slope and how it represents the rate of change of a line. It defines slope as the rise over the run between two points on a line. Positive slope lines rise from left to right, negative slope lines rise from right to left, horizontal lines have zero slope, and vertical lines have undefined slope. The slope formula is defined as the change in y over the change in x between two points.
Mobile Security
The document discusses mobile security and threats to mobile devices. It notes that over 6 billion mobile phones have been sold, most being Android and iPhone devices. It outlines the top threats to mobile devices as data interception, untrusted apps/app stores, and theft/loss of devices. Some potential solutions proposed include anti-malware apps, personal firewalls, anti-spam apps, mobile device management, partitioning data, and monitoring tools.
4.1 notes
The document describes plotting points and graphs on a coordinate plane. It defines an x-axis, y-axis, and four quadrants. Examples of ordered pairs are given with points labeled on the plane. Two linear equations, y=2x-1 and y=-1/3x+2, are shown graphed on the plane with their domains.
Brightidea BOF AMERICAS 2012
The event agenda included presentations on innovation frameworks from Motorola and Chevron, as well as a talk from author Jeffery Phillips. Attendees would participate in breakout sessions on topics like getting started with innovation programs, advanced functionality, executive use cases, and a session called "Innovation Soup" for all levels. The day would conclude with a happy hour networking event to continue discussions among the fellow attendees.
4.6 notes
Two variables show direct variation if their relationship can be written in the form y=ax, where a is the constant of variation. Direct variation equations represent relationships where one variable varies directly as the other changes. To determine if an equation represents direct variation, substitute coordinates to solve for the constant a and rewrite the equation in the form y=ax. The constant of variation and the graphs of direct variation equations can then be used to find output values for given input values.
4.4 notes
Slope represents the rate of change of a line and is calculated by rise over run. A positive slope indicates the line rises from left to right, while a negative slope rises from right to left. Horizontal lines have a slope of zero as there is no rise, and vertical lines have an undefined slope as the run is zero.
4.2 notes
This document discusses how to graph linear equations in a coordinate plane. It defines a linear equation as one whose graph is a line and provides the standard form of a linear equation as ax+by=c. It explains that solutions to linear equations are ordered pairs that make statements true when substituted into the equation. To graph a linear equation, you create a domain of at least three convenient values, solve the equation for those values, and plot the points. Examples are given of graphing the equations y=b, x=a, y=3x-2, y=2.5, and x=-4. The vertical line test is introduced to determine if an equation represents a function.
5 Bare Minimum Things A Web Startup CTO Must Worry About
So you have started-it-up and now you are getting good traffic — Thousands of users, etc. etc.
Do you know script kiddies are scanning your website using simple dictionary attacks on SSH ports? Do you know that once in a while there is a Fatal application Error in your PHP log (which may point to bigger problem)? Do you know that the backup you are taking is actually not gonna restore your DB? Do you know that every night at 12 one of the servers has a CPU spike?
It’s a good idea to catch some of the serious problems early on and deploy tools to proactively assess them. In this session we will discuss some very basic things, as a CTO you MUST worry about and proactively solve problems around them.
These are (in the order of decreasing priority):
1. Security
2. Monitoring/Availability/Load (External/System level)
3. Application errors
4. Backup
5. Source control
Presentation 2008 Lag
The document discusses Northern Ireland's Rural Development Programme from 2007-2013. It allocated over £500 million to improve competitiveness in agriculture/forestry, the environment/countryside, and quality of life. The program was divided into three axes: Axis 1 focused on competitiveness, Axis 2 on the environment, and Axis 3 on quality of life through diversification and tourism. It provided details on the measures under each axis and their targets/budgets. Council clusters were established to deliver the program locally through a model that involved applicants, DARD, Local Action Groups, and a joint administration unit.
Ford Motor Company 1902 Indus Khaitan
What would have Henry Ford done while pitching to his 12 investors trying to raise around $31,000?
This sample business plan template gives an idea about the contents of such presentation while making them understand with a simple example of Ford Motor Company.
Best effort has been made to make sure the data is in sync with the history of Ford Motor Company but may contain factual errors.
Amendment 27
The 27th Amendment regulates congressional pay increases by preventing any increase in pay from taking effect until after the next set of elections, allowing voters to retaliate against increases they view as unjust. It was originally proposed in 1789 as part of the Bill of Rights but was not ratified for over 200 years until 1992. Gregory Watson, a university student, researched the amendment and began a campaign that led to its ratification by 38 states, the final being Michigan.
Disha 2010 Presentation on Entrepreneurship Jan'10 -- Indus Khaitan
This presentation was made to the students of 9th-12th grade in an effort to help them choose alternate career paths.
This presentation was first made in Jan 2010 at the Disha 2010 event held in Bangalore.
NSDC at NASSCOM Product Conclave 2010
NSDC aims to skill 150 million people in India across 20 high growth sectors by 2022. As a public-private partnership, NSDC will provide "viability gap funding" to enable skilling at scale. Key challenges include the lack of precedents for skilling such a large number, a skills gap of over 80%, and 93% of the workforce being in the unorganized sector. To achieve its goal, NSDC will focus on addressing the "imagination gap" through innovative ideas and disruptive technologies that can skill millions in the shortest time and bring excellence on a large scale through customized models. A multi-pronged approach is needed that leverages existing organizations and builds new models through combining different elements.
Practical MySQL
This document discusses best practices for using MySQL in web applications. Some key points include: using MySQL for online web processing (OLWP) rather than OLTP or OLAP; focusing on fast reads over writes; using indexing, composite primary keys, and covering indexes to optimize access patterns; avoiding file sorts and using known ordering; and leveraging the query cache, counts, and paging strategies for performance.
Creating Interactive Olap Applications With My Sql Enterprise And Mondrian Pr...
Julian Hyde presented on creating interactive OLAP applications with MySQL Enterprise and Mondrian. He discussed Mondrian's features like OLAP cubes, MDX queries, and schemas. He also covered olap4j, an API that enables clients to connect to multiple OLAP servers like Mondrian and SQL Server Analysis Services. Case studies showed how Pentaho and Mondrian helped organizations like Frontier Airlines optimize pricing and Loma Linda University provide healthcare analytics.
NSEF India - Why become a social entrepreneur now
The document is a presentation by Indus, an entrepreneur, about becoming an entrepreneur. It lists 5 reasons to become an entrepreneur and 5 qualities needed. It also lists 5 arguments against it and 5 reasons it's a good time. Indus provides contact information and credits various image sources.
Viewers also liked (17)
5 Bare Minimum Things A Web Startup CTO Must Worry About
5 Bare Minimum Things A Web Startup CTO Must Worry About
Disha 2010 Presentation on Entrepreneurship Jan'10 -- Indus Khaitan
Disha 2010 Presentation on Entrepreneurship Jan'10 -- Indus Khaitan
Creating Interactive Olap Applications With My Sql Enterprise And Mondrian Pr...
Creating Interactive Olap Applications With My Sql Enterprise And Mondrian Pr...
Similar to Simple factoring
factoring and the other ones polynomials2.ppt
The document discusses various methods for factoring polynomials:
1) Factoring out the greatest common factor (GCF) of each term.
2) Using the difference of squares formula a2 - b2 = (a + b)(a - b).
3) Grouping terms to produce common binomial factors.
4) Reversing the FOIL process to factor trinomials of the form x2 + bx + c.
5) Factoring polynomials completely by factoring out the GCF and then factoring the remaining terms.
Math083 day 1 chapter 6 2013 fall
This document provides information about a college algebra course taught by Mr. Bianco in Fall 2013. It covers topics like multiplying polynomials using FOIL, factoring polynomials by finding the greatest common factor and factoring trinomials. Examples are provided to demonstrate how to factor polynomials of different forms like ax^2 + bx + c. Students are reminded to check their factoring work by multiplying the factors.
Factoring Polynomials
This document provides instructions on factoring polynomials of various forms:
1) It explains how to factor polynomials by finding the greatest common factor (GCF).
2) It describes how to factor trinomials of the form x2 + bx + c by finding two numbers whose sum is b and product is c.
3) It shows how to factor trinomials of the form ax2 + bx + c by finding factors of a, c whose products and sums satisfy the polynomial.
Factoring
The document discusses various factoring techniques, including:
- Factoring by greatest common factor (GCF)
- Factoring trinomials of the form ax^2 + bx + c by finding two numbers that multiply to c and add to b
- Factoring the difference of two squares and perfect square trinomials
- Using the "box method" to factor trinomials by placing factors of the first and last terms in the boxes
- Factoring by grouping polynomials with four terms into two groups of two terms each.
common monomial factor
The document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by finding the GCF of the numerical coefficients and variable terms. Students are then given practice problems to factor polynomials by finding the GCF and writing the factored form.
March 19, 2014
1) The document discusses different methods for factoring polynomials, including factoring by GCF and factoring by grouping.
2) Factoring by GCF involves finding the greatest common factor of all terms in the polynomial and writing the polynomial as a product with the GCF factored out.
3) Factoring by grouping involves arranging the terms of a four-term polynomial so the first two terms and last two terms each have a common factor, then factoring these common factors out of the pairs of terms.
binomial_theorem_notes.ppt
The document discusses the binomial theorem, which provides a method for expanding binomial expressions of the form (x + y)^n. It explains that each term of the expansion is of the form x^i y^(n-i), with coefficients given by the binomial coefficients. Pascal's triangle is introduced as a way to determine the coefficients. Examples are provided to demonstrate expanding binomial expressions and using the binomial coefficients and theorem.
Factoring Polynomials
This document discusses various methods for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF) of terms in a polynomial.
2) Factoring trinomials of the form x^2 + bx + c by finding two numbers whose product is c and sum is b.
3) Factoring polynomials using grouping when the GCF is not a single term.
4) Recognizing perfect square trinomials and factoring using (a + b)^2 = a^2 + 2ab + b^2.
Algebra 2 Section 5-1
The document discusses operations that can be performed on functions, including addition, subtraction, multiplication, and division. Definitions of each operation are provided, along with examples of applying the operations to specific functions. Addition of functions involves adding the outputs of each function, subtraction involves subtracting the outputs, multiplication involves multiplying the outputs, and division involves dividing the outputs given the denominator function is not equal to 0. Several examples are worked through applying the different operations to functions like f(x)=2x and g(x)=-x+5. The examples also demonstrate evaluating composite functions and restricting domains as needed.
March 6
The document provides a summary of factoring methods:
- Reviewing factoring methods covered such as greatest common factor (GCF) and factoring trinomials
- Announcing that test grades have been posted for one class and quarter grades will be posted for another class tomorrow
- Introducing a new factoring method called "difference of squares" and new Khan Academy topics being added
Grade 8 Mathematics Common Monomial Factoring
The document provides instructions for an individual activity where students must follow 16 directions within 2 minutes to complete tasks like writing their name, drawing shapes, and tapping their desk. It asks what implications the activity might have if directions are not followed properly. The second part of the document provides examples of factoring polynomials using greatest common factor and common monomial factoring methods. It includes practice problems for students to determine the greatest common factor, quotient, and factored form. The document emphasizes following directions and learning different factoring techniques.
11.3
This document provides examples and explanations for multiplying, dividing, and otherwise working with rational expressions. It defines rational expressions as involving polynomials in both the numerator and denominator, with the denominator not equal to 0. Examples are provided for multiplying and dividing rational expressions involving monomials and polynomials. A multi-step word problem is also worked through to find a model for and approximate a baseball player's career batting average as a rational expression involving years played.
best for me1017103 634411962199405000 (2)
This document discusses polynomials and their key properties. It begins by defining a polynomial as an expression constructed using variables, constants, and operations such as addition and multiplication. It then covers the degree of a polynomial and different types of polynomials such as linear, quadratic and cubic. It also discusses the relationship between the zeroes and coefficients of polynomials, including formulas for quadratic and cubic polynomials. Finally, it explains the division algorithm for polynomials and how it can be used to determine if one polynomial is a factor of another.
Factoring polynomials
Factoring is writing a polynomial as a product of two or more polynomials. The main techniques for factoring polynomials are finding the greatest common factor, factoring trinomials of the form ax^2 + bx + c, using special factoring patterns like the difference and sum of squares, and factoring polynomials with four or more terms by grouping. The goal is to factor the polynomial completely into prime factors that cannot be further factored.
Lecture 03 factoring polynomials good one
This document provides an overview of Chapter 13 from a developmental mathematics textbook. It covers factoring polynomials, including:
- Finding the greatest common factor of polynomials
- Factoring trinomials of the form x^2 + bx + c and ax^2 + bx + c
- Checking factored results by multiplying the factors
The chapter sections are described and examples are provided for each type of factoring technique.
Factoring GCF difference of squares.ppt
This document discusses different factoring methods including the greatest common factor method and difference of two squares method. It provides examples of factoring polynomials using each method and emphasizes that the greatest common factor method should always be tried first before other factoring techniques. Students are given practice problems to factor polynomials using these methods and are reminded that sometimes a combination of factoring approaches is needed.
1 1 review on factoring
The document discusses factoring expressions. It defines factoring as rewriting an expression as a product in a nontrivial way. The steps for factoring are: 1) pull out the greatest common factor (GCF), 2) use reverse-FOIL or ac-method for trinomials, 3) use factoring formulas. Examples demonstrate finding the GCF of expressions and factoring out the GCF.
POLYNOMIALS
The document discusses polynomials and polynomial functions. It defines a polynomial as a sum of monomials, with a monomial being a variable or the product of a variable and real numbers with whole number exponents. It classifies polynomials by degree and number of terms, with examples of common types like linear, quadratic, and cubic polynomials. It also defines a polynomial function as a function represented by a polynomial, and discusses finding sums, differences, and writing polynomials in standard form.
Algebra 7 Point 2
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides examples of factoring polynomials by taking out the GCF of 5y2 + 10y + 20, t5 + 8t4 + t3, and 2b4 - 10b3 + 8b2. It also discusses using the distributive property to factor polynomials like 3x2 - 9x + 6.
PowerPoint1
Algebraic expressions can be written in verbal, symbolic, or calculated forms. Verbal expressions use words to represent variables and relations, while symbolic expressions use symbols. To calculate an expression, values are plugged in for the variables and the expression is evaluated. Expressions can also be factored by finding a greatest common factor and grouping like terms.
Similar to Simple factoring (20)
Recently uploaded
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Community pharmacy- Social and preventive pharmacy UNIT 5
Covered community pharmacy topic of the subject Social and preventive pharmacy for Diploma and Bachelor of pharmacy
How to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Recently uploaded (20)
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Simple factoring
- 1. Simple Factoring Objective: Find the greatest common factor in and factor polynomials.
- 5. Distributive Property Examples and Practice To multiply common bases with exponents: Keep the base and add the exponents. x 2 (x 3 ) = x 5 y 4 (y 7 ) = y 11 z 23 (z 3 ) = z 26 Examples: 2(50 + 3) = 100 + 6 = 106 2(x + 3) = 2x + 6 y(x + 1) = yx + y y(x + y 2 ) = yx + y 3 Practice: 3(10 + 6) 3(x + 6) y(x + 6) y(x + y 4 )
- 6. Find the Greatest Common Factor Find the greatest common factor: 10 + 5 2x – 4x 3y +6y 2 8d 3 + 4d 2 + 12d