Saif's project
•Download as PPT, PDF•
0 likes•292 views
The document discusses different methods for factoring different types of expressions: 1) For factoring a binomial, the method is to find the greatest common factor (GCF). 2) For the difference of two perfect squares like x^2 - 16, the method is to break it down and write it as (x - 4)(x + 4). 3) For factoring a trinomial where a is not 1, the method is to use the MFDM (multiply, factor, divide, multiply) approach. If a is 1, the method is to use a "diamond" approach.
Report
Share
Report
Share
![Methods used for each problem ,[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Elimination
This document discusses the elimination/addition method for solving systems of linear equations. It involves eliminating one unknown by adding or subtracting the equations in a way that results in the same unknown having opposite coefficients. This allows the unknown to be eliminated, leaving an equation with only one variable that can be solved for. An example problem demonstrates eliminating the x variable first, then eliminating the y variable to solve the full system of equations. The method is shown to involve multiplying equations by values, adding the equations, and then back-substituting values into one of the original equations.
Ecuaciones 3-grado-ejercicios-resueltos
This document provides examples for solving cubic equations. It explains using the Ruffini rule to factor the polynomial and find the solutions. Several examples are worked out step-by-step, finding 1, -2, and 1/2 as the solutions to one equation. Other examples are provided along with their solutions. Readers are encouraged to work through the examples and ask any questions in the forum.
Suma y resta de fracciones con distinto denominador
This document provides steps for adding fractions with different denominators:
1) Find the lowest common multiple (LCM) of the denominators.
2) Add the numerators and write the sum over the common denominator.
3) Simplify the resulting fraction if possible.
An example problem is worked through applying these steps: 3/6 + 4/10 = 27/30 = 9/10.
Ultimate guide monomials exponents
This document provides an overview and examples for multiplying and dividing monomials with exponents. It defines key terms like monomial, base, and exponent. It explains the product rule for multiplying monomials by adding exponents of the same base. It also explains how to divide monomials by subtracting the exponents of the same base or changing the sign of negative exponents. The document includes 17 examples of multiplying and dividing monomials using these rules.
Power point
To multiply a binomial and a trinomial, you first write them in a box with corresponding terms aligned. You then multiply each term in the first expression with each term in the second. Finally, you combine like terms and arrange the resulting expression from greatest to least exponent.
Cramer’s rule of matrix
Cramer's rule is a method for solving systems of linear equations. It uses determinants to find the solutions for the variables. For two equations with two unknowns, the solutions are found as the ratio of two determinants. For three equations with three unknowns, Cramer's rule can also be applied by writing the solutions as ratios of determinants. Some examples are provided to demonstrate solving systems of two and three equations using Cramer's rule.
3by9on w week_2
This document provides examples for additional homework problems in a statistics course. It discusses problems similar to numbers 11, 13, and 14 from the homework. For problem 11, it explains how to match a regression equation to the correct graph by examining the slope and y-intercept. For problem 13, it demonstrates how to calculate the coefficient of determination from the linear correlation coefficient. Finally, for problem 14 it works through an example of using a multiple regression equation to predict GPA based on given high school GPA and college board scores.
Slide share
1) The document discusses the process of completing the square to solve quadratic equations. It provides examples of factorizing quadratics and using completing the square to solve equations like x^2 - 8x - 7 = 0.
2) The document shows the step-by-step process of completing the square, which involves grouping like terms and adding and subtracting the half of the coefficient of x.
3) Examples are provided to show solving quadratics using completing the square, such as solving 3x^2 - 12x + 9 = 0.
Recommended
Elimination
This document discusses the elimination/addition method for solving systems of linear equations. It involves eliminating one unknown by adding or subtracting the equations in a way that results in the same unknown having opposite coefficients. This allows the unknown to be eliminated, leaving an equation with only one variable that can be solved for. An example problem demonstrates eliminating the x variable first, then eliminating the y variable to solve the full system of equations. The method is shown to involve multiplying equations by values, adding the equations, and then back-substituting values into one of the original equations.
Ecuaciones 3-grado-ejercicios-resueltos
This document provides examples for solving cubic equations. It explains using the Ruffini rule to factor the polynomial and find the solutions. Several examples are worked out step-by-step, finding 1, -2, and 1/2 as the solutions to one equation. Other examples are provided along with their solutions. Readers are encouraged to work through the examples and ask any questions in the forum.
Suma y resta de fracciones con distinto denominador
This document provides steps for adding fractions with different denominators:
1) Find the lowest common multiple (LCM) of the denominators.
2) Add the numerators and write the sum over the common denominator.
3) Simplify the resulting fraction if possible.
An example problem is worked through applying these steps: 3/6 + 4/10 = 27/30 = 9/10.
Ultimate guide monomials exponents
This document provides an overview and examples for multiplying and dividing monomials with exponents. It defines key terms like monomial, base, and exponent. It explains the product rule for multiplying monomials by adding exponents of the same base. It also explains how to divide monomials by subtracting the exponents of the same base or changing the sign of negative exponents. The document includes 17 examples of multiplying and dividing monomials using these rules.
Power point
To multiply a binomial and a trinomial, you first write them in a box with corresponding terms aligned. You then multiply each term in the first expression with each term in the second. Finally, you combine like terms and arrange the resulting expression from greatest to least exponent.
Cramer’s rule of matrix
Cramer's rule is a method for solving systems of linear equations. It uses determinants to find the solutions for the variables. For two equations with two unknowns, the solutions are found as the ratio of two determinants. For three equations with three unknowns, Cramer's rule can also be applied by writing the solutions as ratios of determinants. Some examples are provided to demonstrate solving systems of two and three equations using Cramer's rule.
3by9on w week_2
This document provides examples for additional homework problems in a statistics course. It discusses problems similar to numbers 11, 13, and 14 from the homework. For problem 11, it explains how to match a regression equation to the correct graph by examining the slope and y-intercept. For problem 13, it demonstrates how to calculate the coefficient of determination from the linear correlation coefficient. Finally, for problem 14 it works through an example of using a multiple regression equation to predict GPA based on given high school GPA and college board scores.
Slide share
1) The document discusses the process of completing the square to solve quadratic equations. It provides examples of factorizing quadratics and using completing the square to solve equations like x^2 - 8x - 7 = 0.
2) The document shows the step-by-step process of completing the square, which involves grouping like terms and adding and subtracting the half of the coefficient of x.
3) Examples are provided to show solving quadratics using completing the square, such as solving 3x^2 - 12x + 9 = 0.
Mth 4108-1 b
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) finding measurements of diagonals of a rhombus using its area; (9) determining the number of students in a classroom using time per student; (10) analyzing the height of a hot air balloon over time.
16.4 solving quadratics by completing the square
This document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials like x^2 + 6x + 9 and shows how to find the missing constant term when it is not present. The steps for completing the square to solve an equation are outlined: 1) move all terms to the left side, 2) add the completing the square term to both sides, 3) factor the perfect square trinomial, 4) take the square root of both sides, and 5) solve the resulting equations for x.
Which method is best
This presentation discusses the best methods for solving different types of systems of equations and explains why each method is best. It analyzes three sets of equations: Set A is best solved with elimination because the equations are in standard form and the y-term can be eliminated without multiplying; Set B is best solved with graphing because the equations must be in slope-intercept form to graph; Set C is best solved with substitution because one equation has x alone which can easily be substituted into the second equation.
Completing the square
This document provides instructions for solving quadratic equations by completing the square. It explains the steps: 1) organize the equation terms, 2) add the term to complete the square, 3) factor the perfect square trinomial, 4) take the square root of each side, 5) solve for x. Examples are provided and readers are instructed to work through additional examples on their own.
Week 1 Statistics for Decision (3x9 on Wednesday)
This document provides examples and explanations for 3 extra homework problems from a statistics class.
(1) The first problem asks students to find the range, mean, variance and standard deviation for a sample data set using Minitab software. Step-by-step instructions are given.
(2) The second problem involves interpreting parts of a box-and-whisker plot like minimum, maximum, and quartiles.
(3) The third problem has students match z-scores to points on a histogram by considering where values above, below, or at the mean would fall. An unusual z-score is identified as well.
3by9 On Wednesday for Week 4, Math 221
This document provides examples and solutions for statistics homework problems using binomial, geometric, and Poisson distributions in Minitab software. It addresses three homework problems on finding probabilities for the number of households reporting they feel secure, the number of sales calls required, and the number of hurricanes hitting an island. Step-by-step instructions are given for setting up each problem in Minitab and calculating the requested probabilities. None of the probabilities calculated are described as unusual.
March 20th, 2014
1. The document discusses factoring polynomials. It covers factoring trinomials of the form x^2 + bx + c by finding two binomial factors with a sum of b and product of c.
2. The steps for factoring completely are: look for the greatest common factor, look for special cases like difference of squares or perfect square trinomial, find two different binomial factors if not in a special form, and factor by grouping if there are 4 terms.
3. Examples show factoring trinomials and using the FOIL method in reverse to factor. Factoring requires understanding the relationship between factors and terms in a polynomial.
Week 1 homework help 2015
This document provides examples for 3 homework problems from a statistics class. Problem 18 demonstrates how to calculate the range, mean, variance, and standard deviation of a data set using Minitab software. Problem 22 shows how to identify the minimum, maximum, quartiles, and interquartile range from a box and whisker plot. Problem 24 matches z-scores to a histogram by considering their relationship to the mean and standard deviation.
ty-zha's presentation
This document provides directions on how to factor trinomials into two binomials. It gives the example of factoring x^2 - 5x - 14 and shows the steps of factoring it into (x - 7)(x + 2) by finding the greatest common factor of the terms and grouping the remaining terms.
Solving Quadratics by Completing the Square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Another example problem is worked through to demonstrate the process. Practice problems are provided for the reader to try on their own.
Number Theory
This document contains explanatory answers to 3 sample number theory questions:
1) The value of n will always be odd if the sum of n consecutive integers is 0.
2) Numbers of the form xy0xy (where x and y are digits) will always be divisible by 143 and 77.
3) The remainder when multiplying 3 numbers (where each is of the form 1xxxx) and dividing the product by 14 is 8.
9 6 Factoring Special Polynomials
This document discusses factoring special polynomials, including perfect square polynomials and the difference of two squares. Perfect square polynomials have a first term and last term that are perfect squares, and the middle term is twice the product of the square roots of the first and last terms. The difference of two squares can be factored by taking the square root of the first term and finding the positive and negative factors of the last term.
SUBTRACTION WITHOUT REGROUPING
1) The document describes the steps to subtract two-digit numbers without regrouping: write the numbers with the tens and ones columns aligned, subtract the ones and then tens digits, and check the answer by adding the difference and subtrahend.
2) It provides an example of subtracting 59 - 35 by subtracting the ones (5 - 3 = 2) and tens (9 - 5 = 4) places and writing the difference in the ones place.
3) Students are instructed to complete several practice problems subtracting two-digit numbers without regrouping and to check their work.
Polynomials
This document provides information about polynomials including:
1. Defining polynomials as the sum of monomials and stating that expressions with variables in the denominator are not polynomials.
2. Examples of determining if expressions are polynomials and finding the degree of monomials and polynomials.
3. Explaining ascending and descending order and examples of rearranging polynomial terms in ascending and descending order.
Writing linear equations KG Math Middle School
The document provides information about graphing and writing linear equations in slope-intercept form (y=mx+b). It defines slope and y-intercept, and explains how to graph lines by using the slope and y-intercept. It also demonstrates how to write an equation of a line when given the slope and y-intercept, a point and the slope, or two points. Key steps include finding the slope using the formula (m=(y2-y1)/(x2-x1)), setting up and solving equations to find the y-intercept, and plugging the slope and y-intercept into the slope-intercept form to write the equation.
Big M method
The document describes the Big-M method, a variation of the simplex method for solving linear programming problems with "greater-than" or "equal-to" constraints. It involves adding artificial variables to obtain an initial feasible solution, using a large value M for each artificial variable. The transformed problem is then solved via simplex method to eliminate artificial variables. Examples are provided to illustrate the step-by-step process. Potential drawbacks discussed are how large M should be and not knowing feasibility until optimality is reached.
Multistep Equations Basics
This document provides steps for solving multi-step equations in 3 or fewer steps:
1. Clear the equation of fractions and decimals.
2. Use the Distributive Property to remove parenthesis on each side.
3. Combine like terms on each side.
4. Undo addition or subtraction.
5. Undo multiplication or division.
Quardatic equation
This document defines a quadratic equation as one that contains an unknown quantity squared but not to higher powers, and provides the standard form ax^2 + bx + c = 0. It lists three methods for solving quadratic equations: factorization, completing the square, and the quadratic formula. An example problem is worked out step-by-step to show solving a quadratic equation using factorization.
Integrated Literature And Math Activity
The document contains three short passages about fish, camels, and ants respectively. Each passage poses a riddle or question about counting the animals pictured and identifying their habitat. Students are instructed to solve the riddles using the pictures provided.
Factoring Binomial, Difference Of Two Perfect Squares
To factor a trinomial when a does not equal 1, follow the steps of MFDM:
1. Multiply using the distributive property
2. Factor out the greatest common factor
3. Divide the remaining terms and group into binomials
Scientific skill
The document summarizes the history and key facts about dinosaurs. It discusses how scientists first began studying dinosaur bones in the 1820s and how Sir Richard Owen coined the term "dinosaur" in 1842. It describes how dinosaurs have since been divided into orders, genera, and species. Some dinosaurs were bipedal, others quadrupedal, and they exhibited a wide range of behaviors and traits. The document also summarizes theories about what caused the mass extinction of dinosaurs 65 million years ago.
Global Math Game Guideline English Version
Global Math Game Guideline English Version
Global Math Description of Game Development Process
(from planning to release)
More Related Content
What's hot
Mth 4108-1 b
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) finding measurements of diagonals of a rhombus using its area; (9) determining the number of students in a classroom using time per student; (10) analyzing the height of a hot air balloon over time.
16.4 solving quadratics by completing the square
This document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials like x^2 + 6x + 9 and shows how to find the missing constant term when it is not present. The steps for completing the square to solve an equation are outlined: 1) move all terms to the left side, 2) add the completing the square term to both sides, 3) factor the perfect square trinomial, 4) take the square root of both sides, and 5) solve the resulting equations for x.
Which method is best
This presentation discusses the best methods for solving different types of systems of equations and explains why each method is best. It analyzes three sets of equations: Set A is best solved with elimination because the equations are in standard form and the y-term can be eliminated without multiplying; Set B is best solved with graphing because the equations must be in slope-intercept form to graph; Set C is best solved with substitution because one equation has x alone which can easily be substituted into the second equation.
Completing the square
This document provides instructions for solving quadratic equations by completing the square. It explains the steps: 1) organize the equation terms, 2) add the term to complete the square, 3) factor the perfect square trinomial, 4) take the square root of each side, 5) solve for x. Examples are provided and readers are instructed to work through additional examples on their own.
Week 1 Statistics for Decision (3x9 on Wednesday)
This document provides examples and explanations for 3 extra homework problems from a statistics class.
(1) The first problem asks students to find the range, mean, variance and standard deviation for a sample data set using Minitab software. Step-by-step instructions are given.
(2) The second problem involves interpreting parts of a box-and-whisker plot like minimum, maximum, and quartiles.
(3) The third problem has students match z-scores to points on a histogram by considering where values above, below, or at the mean would fall. An unusual z-score is identified as well.
3by9 On Wednesday for Week 4, Math 221
This document provides examples and solutions for statistics homework problems using binomial, geometric, and Poisson distributions in Minitab software. It addresses three homework problems on finding probabilities for the number of households reporting they feel secure, the number of sales calls required, and the number of hurricanes hitting an island. Step-by-step instructions are given for setting up each problem in Minitab and calculating the requested probabilities. None of the probabilities calculated are described as unusual.
March 20th, 2014
1. The document discusses factoring polynomials. It covers factoring trinomials of the form x^2 + bx + c by finding two binomial factors with a sum of b and product of c.
2. The steps for factoring completely are: look for the greatest common factor, look for special cases like difference of squares or perfect square trinomial, find two different binomial factors if not in a special form, and factor by grouping if there are 4 terms.
3. Examples show factoring trinomials and using the FOIL method in reverse to factor. Factoring requires understanding the relationship between factors and terms in a polynomial.
Week 1 homework help 2015
This document provides examples for 3 homework problems from a statistics class. Problem 18 demonstrates how to calculate the range, mean, variance, and standard deviation of a data set using Minitab software. Problem 22 shows how to identify the minimum, maximum, quartiles, and interquartile range from a box and whisker plot. Problem 24 matches z-scores to a histogram by considering their relationship to the mean and standard deviation.
ty-zha's presentation
This document provides directions on how to factor trinomials into two binomials. It gives the example of factoring x^2 - 5x - 14 and shows the steps of factoring it into (x - 7)(x + 2) by finding the greatest common factor of the terms and grouping the remaining terms.
Solving Quadratics by Completing the Square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Another example problem is worked through to demonstrate the process. Practice problems are provided for the reader to try on their own.
Number Theory
This document contains explanatory answers to 3 sample number theory questions:
1) The value of n will always be odd if the sum of n consecutive integers is 0.
2) Numbers of the form xy0xy (where x and y are digits) will always be divisible by 143 and 77.
3) The remainder when multiplying 3 numbers (where each is of the form 1xxxx) and dividing the product by 14 is 8.
9 6 Factoring Special Polynomials
This document discusses factoring special polynomials, including perfect square polynomials and the difference of two squares. Perfect square polynomials have a first term and last term that are perfect squares, and the middle term is twice the product of the square roots of the first and last terms. The difference of two squares can be factored by taking the square root of the first term and finding the positive and negative factors of the last term.
SUBTRACTION WITHOUT REGROUPING
1) The document describes the steps to subtract two-digit numbers without regrouping: write the numbers with the tens and ones columns aligned, subtract the ones and then tens digits, and check the answer by adding the difference and subtrahend.
2) It provides an example of subtracting 59 - 35 by subtracting the ones (5 - 3 = 2) and tens (9 - 5 = 4) places and writing the difference in the ones place.
3) Students are instructed to complete several practice problems subtracting two-digit numbers without regrouping and to check their work.
Polynomials
This document provides information about polynomials including:
1. Defining polynomials as the sum of monomials and stating that expressions with variables in the denominator are not polynomials.
2. Examples of determining if expressions are polynomials and finding the degree of monomials and polynomials.
3. Explaining ascending and descending order and examples of rearranging polynomial terms in ascending and descending order.
Writing linear equations KG Math Middle School
The document provides information about graphing and writing linear equations in slope-intercept form (y=mx+b). It defines slope and y-intercept, and explains how to graph lines by using the slope and y-intercept. It also demonstrates how to write an equation of a line when given the slope and y-intercept, a point and the slope, or two points. Key steps include finding the slope using the formula (m=(y2-y1)/(x2-x1)), setting up and solving equations to find the y-intercept, and plugging the slope and y-intercept into the slope-intercept form to write the equation.
Big M method
The document describes the Big-M method, a variation of the simplex method for solving linear programming problems with "greater-than" or "equal-to" constraints. It involves adding artificial variables to obtain an initial feasible solution, using a large value M for each artificial variable. The transformed problem is then solved via simplex method to eliminate artificial variables. Examples are provided to illustrate the step-by-step process. Potential drawbacks discussed are how large M should be and not knowing feasibility until optimality is reached.
Multistep Equations Basics
This document provides steps for solving multi-step equations in 3 or fewer steps:
1. Clear the equation of fractions and decimals.
2. Use the Distributive Property to remove parenthesis on each side.
3. Combine like terms on each side.
4. Undo addition or subtraction.
5. Undo multiplication or division.
Quardatic equation
This document defines a quadratic equation as one that contains an unknown quantity squared but not to higher powers, and provides the standard form ax^2 + bx + c = 0. It lists three methods for solving quadratic equations: factorization, completing the square, and the quadratic formula. An example problem is worked out step-by-step to show solving a quadratic equation using factorization.
What's hot (18)
Viewers also liked
Integrated Literature And Math Activity
The document contains three short passages about fish, camels, and ants respectively. Each passage poses a riddle or question about counting the animals pictured and identifying their habitat. Students are instructed to solve the riddles using the pictures provided.
Factoring Binomial, Difference Of Two Perfect Squares
To factor a trinomial when a does not equal 1, follow the steps of MFDM:
1. Multiply using the distributive property
2. Factor out the greatest common factor
3. Divide the remaining terms and group into binomials
Scientific skill
The document summarizes the history and key facts about dinosaurs. It discusses how scientists first began studying dinosaur bones in the 1820s and how Sir Richard Owen coined the term "dinosaur" in 1842. It describes how dinosaurs have since been divided into orders, genera, and species. Some dinosaurs were bipedal, others quadrupedal, and they exhibited a wide range of behaviors and traits. The document also summarizes theories about what caused the mass extinction of dinosaurs 65 million years ago.
Global Math Game Guideline English Version
Global Math Game Guideline English Version
Global Math Description of Game Development Process
(from planning to release)
Jeopardymathmapgles
This math jeopardy review activity contains 50 questions about various math topics ranging from number sentences to word problems to geometry shapes. The questions are multiple choice or require writing a mathematical expression. For each question, the user selects an answer and is informed if it is correct or not before moving on to the next question.
Minimal pairs
This document provides a list of minimal pairs, which are pairs of words that differ by only one phoneme, to be used in a five minute activity to practice distinguishing similar sounds. It contains 40 pairs of words like "rocks" and "socks" that vary in only their initial consonant sounds to help listeners differentiate between sounds like "r" and "s". A link is also included to access additional pages of minimal pair word lists for further phonetic practice.
The pre algebra math fair and family activity project
This document provides information about a family math activity and math fair for students. It includes an overview of the family math activity, which involves students working with their families at home on math questions and creating a display about their answers. It also describes the math fair, where families can see student displays and participate in math demonstrations and activities. The document provides examples and guidance to help families engage with math concepts like using coordinates to plot points on a graph.
Viewers also liked (7)
Factoring Binomial, Difference Of Two Perfect Squares
Factoring Binomial, Difference Of Two Perfect Squares
The pre algebra math fair and family activity project
The pre algebra math fair and family activity project
Similar to Saif's project
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.
Factoring Polynomials (1).pptx
The document discusses factoring polynomials and finding the roots of polynomial equations. It defines polynomials and polynomial equations. It then covers several methods for factoring polynomials, including factoring polynomials with a common monomial factor, factoring polynomials that are a difference of squares, factoring trinomials, and factoring polynomials by grouping. It also discusses using the factors to find the solutions or roots of a polynomial equation, which are also known as the zeros of a polynomial function.
1.5 Quadratic Equations (Review)
This document provides instruction on factoring quadratic equations. It begins by reviewing factoring polynomials and trinomials. It then discusses factoring binomials using difference of squares, sum/difference of cubes, and other patterns. Finally, it explains that a quadratic equation can be solved by factoring if it can be written as a product of two linear factors. An example demonstrates factoring a quadratic equation by finding the two values that make each factor equal to zero.
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.
Factoring Reviewed
Factoring for non-math lovers. This slide presentation is designed to help remove some of the stress out of factoring at t he Algebra 2 level.
Factoring
The document discusses three methods for factoring expressions:
1) Factoring trinomials where a is not equal to 1 using the My Friend Does Math (MFDM) method of multiplying, factoring out, and dividing.
2) Factoring trinomials where a is equal to 1 using the diamond method.
3) Solving two perfect squares by factoring them using the formula (a-b)(a+b) and plugging the results into parentheses.
Factoring of Perfect Square Trinomial.pptx
This document provides information and examples on factoring perfect square trinomials. It defines a perfect square trinomial as a polynomial that can be factored into the square of a binomial. It outlines the criteria for identifying a perfect square trinomial, which are: 1) it must have three terms, 2) the first term must be a perfect square, 3) the third term must be a perfect square, and 4) the middle term must be twice the product of the square roots of the first and last terms. The document provides examples of factoring perfect square trinomials and has students practice identifying and factoring perfect square trinomials.
1.5 Quadratic Equations.pdf
This document provides instruction on factoring polynomials and quadratic equations. It begins by reviewing factoring techniques like finding the greatest common factor and factoring trinomials and binomials. Examples are provided to demonstrate the factoring methods. The document then discusses solving quadratic equations by factoring, putting the equation in standard form, and setting each factor equal to zero. An example problem demonstrates solving a quadratic equation through factoring. The document concludes by assigning homework and an optional reading for the next class.
GR 8 Math Powerpoint about Polynomial Techniques
-This is a powerpoint inspired by one of Canva displayed presentation.
- This is about Math Polynomials and good for highschoolers presentation for school.
- It consists of 39 pages explaining each of the Polynomial Techniques.
- Good for review or inspired powerpoint.
Factoring Polynomials in Modular Approach
The document provides lessons on factoring polynomials with common monomial factors and the difference of two squares. It explains that to factor polynomials with common monomial factors, one must find the greatest common factor (GCF) and divide each term by the GCF. It also explains that to factor the difference of two squares, one must get the square root of each term and use those roots to form the sum and difference as factors. Examples are provided to demonstrate these factoring techniques step-by-step. The document aims to teach learners how to completely factor different types of polynomials.
Factoring
This document provides an overview of different factoring techniques for quadratics, including:
1) Looking for patterns in the terms like perfect squares or a variable being cubed to use shortcuts.
2) Using the greatest common factor when there are only two terms or the coefficient of x is greater than 1.
3) Factoring the difference of squares or perfect square trinomials using their respective shortcuts.
4) Completely factoring polynomials using the generic rectangle/diamond method or variations for more complex expressions.
Right And Wrong’S Of Pre Calculus
The document provides examples of common mistakes made when working with exponents, radicals, polynomials, rational expressions, and solving equations in pre-calculus. It demonstrates incorrect work and explains the errors, such as adding instead of multiplying terms with exponents or failing to square both sides of an equation when taking the square root of each side. Key concepts are reviewed, such as factoring polynomials before simplifying rational expressions or dividing terms. Helpful formulas are also listed, such as the quadratic formula.
March 7
1. The document discusses factoring perfect square trinomials, which are polynomials where the first term is a perfect square, the third term is a perfect square, and the coefficient of the second term is twice the square root of the product of the first and third term coefficients.
2. To factor a perfect square trinomial, take the square root of the first term, add it to the square root of the third term, and place it in parentheses twice to get the two factors.
3. Examples are provided of determining if a trinomial is a perfect square and factoring perfect square trinomials like x2 + 10x + 25 as (x + 5)2.
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
This document provides information about different methods for solving quadratic equations. It discusses factoring the equation, using the quadratic formula, and completing the square. Step-by-step explanations are provided for each method. Factoring involves finding two binomials that multiply to give the quadratic term and add to the linear term. The quadratic formula is given as x = (-b ±√(b2 - 4ac))/2a. Completing the square requires grouping like terms and completing the square of the quadratic term.
Mathnasium Presentation (1)
This document provides an outline for teaching various factoring techniques. It begins with definitions of algebraic expressions, polynomials, factors, and factoring. It then covers finding the greatest common factor, factoring by using the GCF, factoring by grouping, factoring differences of squares, factoring perfect square trinomials using the special formula, and solving word problems using factoring. Examples are provided for each technique to demonstrate how to factor different polynomial expressions. Special cases like the sum and difference of cubes are also discussed. The document concludes with an explanation of the quadratic formula.
4.4 day 1
This document provides instructions on factoring quadratic expressions. It discusses factors, factoring, factoring trinomials of the form ax^2 + bx + c, checking factors using FOIL, and factoring expressions with a greatest common factor. It also introduces the arc method for factoring trinomials where the leading coefficient is not 1, including arcing the leading term, factoring, dividing by the arced coefficient, simplifying, and undoing the arc. Examples are provided to demonstrate each of these factoring techniques.
Notes solving polynomial equations
The document provides information about solving polynomial equations. There are three main ways to solve polynomial equations: 1) Using factoring and the zero product property, 2) Using a graphing calculator to graph the equation, and 3) Using synthetic division. The maximum number of solutions a polynomial equation can have is equal to the degree of the polynomial. Examples are provided to demonstrate solving polynomial equations by factoring.
Q1-W1-Factoring Polynomials.pptx
This document provides instruction on factoring polynomials. It covers several factoring methods including common monomial factoring, difference of squares, sum and difference of cubes, perfect square trinomials, and general trinomials. Examples are provided for each method. The objectives are to determine appropriate factoring methods, factor polynomials completely using various techniques, and solve problems involving polynomial factors.
Uas teori bil.
Fermat's Little Theorem states that if p is a prime and a does not divide p, then a^p-1 is congruent to 1 modulo p. Using this, we can reduce exponents modulo p. Here, 7 is prime and 3 does not divide 7, so 3^6 is congruent to 1 modulo 7. Since 999999999 = 16666666*6 + 3, we can reduce the exponent to get 3^999999999 is congruent to 3^3, which is congruent to 6 modulo 7.
Factoring polynomials with common monomial factor
This document discusses factoring polynomials by finding the greatest common factor (GCF). It provides a strategy for finding the GCF which involves finding the greatest common factor of numerical coefficients and the variable with the least exponent appearing in each term. The GCF is then the product of these common factors. Examples are provided of factoring polynomials by dividing the polynomial by its GCF. The document also contains practice problems for students to complete involving factoring polynomials using the GCF method.
Similar to Saif's project (20)
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
More from daisyrock
Abby's project 1
The document discusses different types of algebraic expressions and how to factor them. It explains that a binomial contains two terms, and when factoring a binomial you write each term twice. A trinomial contains three terms and requires factoring using a diamond method. The difference of two perfect squares involves subtracting two terms that are perfect squares of the same base. A polynomial is the sum of monomial terms and needs to be simplified by factoring out common terms.
Factoring
This document discusses different types of factoring expressions including trinomials, binomials, and polynomials. Trinomials have three terms and require factoring out the greatest common factor. Binomials can be factored in four ways and using the FOIL method when multiplying two binomials. Polynomials are expressions with constants, variables, and exponents combined using addition, subtraction, and multiplication.
Factoring
This document discusses different types of factoring expressions including trinomials, binomials, and polynomials. Trinomials have three terms and require factoring out the greatest common factor. Binomials can be factored in four ways and using the FOIL method when multiplying two binomials. Polynomials are expressions with constants, variables, and exponents combined using addition, subtraction, and multiplication.
My Favorite Factoring Method
This document discusses Lisa Abreu's favorite factoring method. It provides a brief history of factoring, noting that Hermann Grassmann was an early pioneer. It also explains the purposes of factoring, such as simplifying expressions and making them easier to understand. Lisa then provides examples of factoring a trinomial using the "Two Binomial Method" and factoring the difference of two squares. She concludes that factoring helps connect algebra to linear algebra and makes math more fun.
Factoring Binomial, Difference Of Two Perfect Squares
My Friend Does Math is a mnemonic device to remember the steps for factoring a trinomial when a does not equal 1: (1) multiply using the distributive property, (2) factor out the greatest common factor, (3) divide the remaining terms by the factorized greatest common factor. The steps are: multiply, factor out, divide, and multiply.
JALEN"S TURTORIAL
Jalen Deleon provides a tutorial on factoring binomials and trinomials. His method for factoring binomials is to find the greatest common factor. He also explains how to factor the difference of two perfect squares by breaking them down and putting the answer in parentheses. For trinomials, he uses the "diamond method" taught by his teacher Ms. Suhker. He provides examples of factoring 4j4-8 and D2-16 to demonstrate his methods.
Integrated project
This project requires students to create a slideshow explaining how to factor different types of polynomials. Students must include examples of factoring binomials, differences of squares, and trinomials where a is and is not 1. For each example, students must show the factoring method used and explain each step. Students will upload their slideshows to a class blog and submit a hard copy for evaluation. The project aims to make math more engaging for students and develop their math and technology skills.
Integrated Project
This project requires students to create a slideshow explaining how to factor different types of polynomials. Students must include examples of factoring binomials, differences of squares, and trinomials where a is and is not 1. For each example, students must show the factoring method used and explain each step. Students will upload their slideshows to a class blog and submit a hard copy for evaluation. The project aims to make math more engaging for students and develop their math and technology skills.
Think like a teacher
The teacher is asking students to grade sample student work from a fictional math problem to understand partial credit. The problem is worth 4 points total. Students should consider whether to award partial credit for a correct formula even with a mathematical error, value the answer or method more, handle small arithmetic errors, and grade an answer with no shown work. Students must justify their grading and thoughts on what is fair.
Kristi's Trig. for Dummies
The document provides an overview of key concepts in trigonometry, including definitions of right triangles, trigonometric functions, the unit circle, and conversions between degrees and radians. It explains trigonometric identities like SOH CAH TOA, reference angles, coterminal angles, and reciprocals. The summary covers trigonometry basics, relationships between angles and sides of triangles, and the unit circle model for defining trig functions.
Angel
Trigonometry for Dummies provides an overview of trigonometric functions and how to measure angles. It defines the sine, cosine, and tangent functions using a right triangle and unit circle. Angles can be measured in degrees or radians, with radians defined as the intercepting arc of a central angle over the radius of a circle. The trigonometric functions are also defined in terms of their coordinates on a unit circle. Common trigonometric identities are presented relating functions like sine, cosine, cosecant, secant, and cotangent.
presentation
1) Radians are a way of measuring angles based on the length of an arc along a circle. To convert radians to degrees, multiply the radian measurement by 180/π.
2) Reference angles are always acute angles formed between the terminal side of a given angle and the x-axis.
3) Coterminal angles are angles that share the same initial and terminal sides and thus represent the same angle position on a unit circle.
Trigonometry[1]
Trigonometry deals with the sides and angles of triangles and their relationships. It is used in fields like science, business, music, and by professionals like tidal experts and meteorologists. Key concepts in trigonometry include the sine, cosine, and tangent functions, radian measurement, reference angles, quadrants, and the unit circle. Trigonometric functions can be added, subtracted, and multiplied following specific rules.
Trigonometry For
This document provides an introduction to basic trigonometry terms and concepts:
1. It defines clockwise and counterclockwise rotation, and explains that angles can be measured in degrees or radians.
2. A unit circle is introduced as a circle with radius of 1 on the coordinate plane, and how sine, cosine, and tangent values can be found using triangles on the unit circle.
3. Reference angles and coterminal angles are defined in relation to the terminal side of an angle and the x-axis on the unit circle.
4. Some special angles that have exact trigonometric function values are mentioned. Basic trigonometric identities for cosecant and secant are also provided
Trig For Dummies By Adrian P.
Trigonometry deals with relationships between sides and angles of triangles. It uses basic formulas relating opposite, adjacent, and hypotenuse sides to trigonometric functions of an angle. These formulas apply to right triangles and can be extended to any angle using concepts like reference angles, coterminal angles, radians, and the unit circle. Mastering basic trigonometric functions, special angle values, and identities provides the foundation for applying trigonometry to solve problems.
Trigonometry For Dummies by ItzelS
This document provides an introduction to trigonometry by defining key terms and concepts. It explains that trigonometry deals with angles and sides of triangles. It then introduces reference angles as the acute angle formed by the terminal side and x-axis, and how to find a reference angle by subtracting an obtuse angle from 180 or 360 degrees. It also defines coterminal angles as angles that share the same initial and terminal sides, and can be positive or negative depending on the direction of rotation. Finally, it briefly outlines sine, cosine, and tangent on the unit circle and their relationships.
Ms.Sukher-natalie f.
1) Trigonometry deals with relationships between the sides and angles of triangles, especially right triangles.
2) There are specific trigonometric functions (sine, cosine, tangent) that relate a particular side of a right triangle to an angle of the triangle.
3) Co-terminal angles are angles that have the same terminal side when drawn in standard position, while reference angles are always between 0 and 90 degrees and represent the smallest angle formed between the terminal side and the x-axis.
Math Project
The document defines and provides properties of a rhombus. A rhombus is a four-sided shape where all sides have equal length and opposite sides are parallel. The properties include that the diagonals bisect each angle, opposite angles are equal, the sum of the interior angles is 360 degrees, and opposite sides are parallel. Any two consecutive internal angles are supplementary. The area formula is A=BH/2 and the perimeter formula is P=LW.
Special Parallelograms
This document defines and provides properties of four special types of parallelograms: rectangles have four right angles and opposite sides that are parallel and congruent; rhombuses have all sides that are congruent and diagonals that bisect each other perpendicularly; squares are rhombuses with four right angles; and general parallelograms have two sets of parallel and congruent sides, opposite angles that are congruent, and diagonals that bisect each other and form two congruent triangles. It also gives formulas for perimeter and area.
More from daisyrock (20)
Factoring Binomial, Difference Of Two Perfect Squares
Factoring Binomial, Difference Of Two Perfect Squares
Saif's project
- 1. Factoring How to Factor a binomial, find the difference of two perfect squares, Factoring a trinomial with a is not 1 and a is one