7 3 Zero Product Property A
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1. The document presents problems involving solving equations for x and factoring expressions to find values of x that make the expression equal to zero. It discusses using the zero product property (ZPP), where the product of two numbers is zero if one or both numbers is zero. Students are asked to factor expressions using the greatest common factor (GCF) and using factoring, then apply ZPP to find solutions for x. Graphing an expression is used to visualize where it crosses the x-axis, relating to solutions found earlier. 2. Students are asked to factor equations using GCF or factoring techniques, then apply ZPP to find the solutions to each equation. 3. The document provides practice with
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7 4 Notes A
This document contains instructions and examples for solving various algebra problems involving factoring expressions and equations. It is divided into three topics: 1) greatest common factor and the distributive property, 2) greatest common factor and zero product property with solving equations, and 3) more factoring. Students are asked to work through sample problems with a partner and be prepared to share their work. They will then schedule appointments with other students to review specific problem sets related to each topic.
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The student will be able to solve systems of equations using elimination with addition and subtraction. There are 5 steps to solving a system by elimination: 1) put the equations in standard form, 2) determine which variable to eliminate, 3) add or subtract the equations to eliminate the variable, 4) plug back into one equation to find the other variable, and 5) check the solution by substituting into both original equations. Two examples are provided to demonstrate the process.
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MATH : EQUATIONS
1. If x/5 - 3 = 9 then x = 20
2. Solve: 3x/4 + 9 = 21 then x = 12
3. If 2x/7 - 5 = 2 then x = 14
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3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
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8th alg -l6.4--jan28
1. The document provides instructions and examples for solving systems of equations using elimination.
2. It explains that you may need to multiply one or both equations by a number to get opposite terms that can be eliminated. Then you add the equations to solve for one variable, substitute to solve for the other, and write the solution as an ordered pair.
3. Several examples of systems of equations are given and students are instructed to use elimination to solve them.
8th alg -l3.2--nov1
1) The document provides instructions for a math lesson assignment on linear functions and solving equations. Students are to complete practice problems from their textbook and sign up for extra credit on an earlier test.
2) The warmup exercises involve solving various equations algebraically. The lesson defines linear functions and their relationship to roots/zeros, discussing how to graphically and algebraically solve linear equations by setting them equal to zero.
3) Examples are shown of solving equations both graphically by sketching the line and algebraically by isolating the variable, such as solving 0 = 1/2x - 2 for x = 4.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
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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.
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Multiplying polynomials can be done using three methods:
1. The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2. FOIL (First, Outer, Inner, Last), which is a shortcut used for multiplying two binomials by multiplying the first, outer, inner, and last terms.
3. The box method, which involves drawing a box and writing one polynomial above and beside the box before distributing the multiplication similar to the distributive property.
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The student will learn to solve systems of equations using elimination with addition and subtraction. This involves putting the equations in standard form, eliminating one variable by adding or subtracting the equations, solving for the eliminated variable, plugging back into one equation to solve for the other variable, and checking the solution. Two examples are shown of solving systems of two equations with two variables using this elimination method.
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The student will be able to solve systems of equations using elimination with addition and subtraction. There are 5 steps to solving a system by elimination: 1) put the equations in standard form, 2) determine which variable to eliminate, 3) add or subtract the equations to eliminate the variable, 4) plug back into one equation to find the other variable, and 5) check the solution by substituting into both original equations. Two examples are provided to demonstrate the process.
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1. If x/5 - 3 = 9 then x = 20
2. Solve: 3x/4 + 9 = 21 then x = 12
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1) The distributive property, which involves multiplying each term of one polynomial with each term of the other.
2) FOIL (First, Outer, Inner, Last), which is a mnemonic for multiplying binomials by multiplying corresponding terms.
3) The box method, which involves drawing a box and writing one polynomial above and beside the box, then multiplying corresponding terms. Examples are provided to demonstrate each method.
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The document discusses three methods for multiplying polynomials: the distributive property, FOIL (First, Outer, Inner, Last), and the box method. It provides examples of multiplying polynomials using each method. The key steps of FOIL are to multiply the first, outer, inner, and last terms of each binomial being multiplied. The box method involves drawing a box and writing one polynomial above and beside the box before multiplying the terms. The document emphasizes that all three methods will provide the same answer when multiplying polynomials.
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1. The document provides instructions and examples for solving systems of equations using elimination.
2. It explains that you may need to multiply one or both equations by a number to get opposite terms that can be eliminated. Then you add the equations to solve for one variable, substitute to solve for the other, and write the solution as an ordered pair.
3. Several examples of systems of equations are given and students are instructed to use elimination to solve them.
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1) The document provides instructions for a math lesson assignment on linear functions and solving equations. Students are to complete practice problems from their textbook and sign up for extra credit on an earlier test.
2) The warmup exercises involve solving various equations algebraically. The lesson defines linear functions and their relationship to roots/zeros, discussing how to graphically and algebraically solve linear equations by setting them equal to zero.
3) Examples are shown of solving equations both graphically by sketching the line and algebraically by isolating the variable, such as solving 0 = 1/2x - 2 for x = 4.
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4 7 Notes A
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2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
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Here are the key steps to factoring when a ≠ 1:
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4. Factor using the box method, finding the GCF of each row and column.
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3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
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.
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.
Solving polynomial equations in factored form
The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x – 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x – 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
College Algebra 1.4
This document provides instructions on solving quadratic equations using different methods: factoring, extracting square roots, the quadratic formula, and determining the discriminant. It explains that if the product of two terms is zero, one of the terms must be zero. This is used to solve equations by setting each factor equal to zero. Examples are provided to demonstrate solving quadratic equations by factoring, taking the square root of both sides, and using the discriminant to determine the number of solutions.
Chapter 3. linear equation and linear equalities in one variables
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
Zeros of p(x)
This document discusses various methods for finding the zeros or roots of polynomial functions, including factoring, factor theorem, synthetic division, and using the principle that every polynomial of degree n has n zeros. It provides examples of finding the zeros of polynomials by factorization, using a given zero to find other zeros through synthetic division, and identifying which numbers are zeros of various polynomials. Exercises are included for students to practice finding remaining zeros given one zero and identifying polynomial factors.
March 9, 2015
Today's math lesson covers dividing polynomials by monomials and multiplying binomials. Students should bring good notes and their full attention. The warm-up reviews solving binomial equations and discount word problems. Methods for multiplying binomials include the box method and FOIL (First, Outer, Inner, Last). Patterns emerge depending on the signs of terms. Dividing polynomials begins with dividing each term in the numerator by the monomial denominator. Students should take complete, easy to read notes on multiplying and dividing polynomials.
Math project
The document summarizes reflections from Patrick Hyatt and Quincie McCalla on a project where they created complex math problems to review concepts they had learned. Both note that while the project provided some review, it took a significant amount of time to develop the problems and stretched their understanding too far at times. They suggest modifying the format of the project to have students work in pairs and take responsibility for specific concepts, then present problems to each other, for a more focused review that clarifies misunderstandings.
2.2 Polynomial Function Notes
The document discusses polynomial functions, including how to graph common polynomials, find zeros of polynomials, and write polynomials given their roots. It provides examples of matching polynomial equations to their graphs, finding the real zeros of polynomials by factoring, and writing polynomials when given the roots. The document also covers how to use a graphing calculator to find the zeros of polynomials.
Solving Quadratic Equations by Factoring
The document discusses solving quadratic equations by factoring. It provides examples of factoring quadratic expressions to find the solutions to the equations. These include using the zero product rule, factoring a common factor, and factoring a perfect square. It also provides two word problems involving consecutive integers and the Pythagorean theorem and shows how to set up and solve the quadratic equations derived from the word problems.
10.4
Here are the steps to solve each equation by graphing:
1) x2 + 5x + 6 = 0
Write in standard form: x2 + 5x + 6 = 0
Graph the related function y = x2 + 5x + 6. The x-intercepts are the solutions, which are -3 and -2.
2) x2 + 8x + 16 = 0
Write in standard form: x2 + 8x + 16 = 0
Graph the related function y = x2 + 8x + 16. The x-intercepts are the solutions, which are -4 and -4.
3) x2 - 2x + 3 = 0
Write in standard
Detailed Lesson Plan in Mathematics
This lesson plan outlines how to teach 7th grade students to multiply polynomials. It includes objectives, subject matter, procedures, and assessment. Students will learn to multiply monomials, binomials, and polynomials with multiple terms using distribution and combining like terms. Examples are provided for multiplying different combinations of monomials and binomials. A review, lesson, and problem solving section are included in the procedures. The assessment evaluates students' understanding of defining polynomials and multiplying different polynomial expressions.
Finding a polyomial from data
This document covers how to find a polynomial function given certain data like the zeroes, y-intercept, end behavior, and multiplicity.
Simplifying Basic Rational Expressions Part 1
This document provides instructions and examples for simplifying rational expressions by factoring and canceling terms. It begins with definitions of rational expressions and undefined values. Examples shown include finding excluded values that make expressions undefined, as well as simplifying expressions by factoring numerators and denominators and canceling common factors. The goal is to either find excluded values or simplify the expressions into their lowest terms. Ten problems with step-by-step solutions are provided to demonstrate the techniques.
Similar to 7 3 Zero Product Property A (20)
Chapter 3. linear equation and linear equalities in one variables
Chapter 3. linear equation and linear equalities in one variables
More from mbetzel
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations (translations, reflections, rotations, and dilations) and provides examples of identifying each type using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.6 2.7 notes a
1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations.
2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined.
3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages. Finally, it addresses solving an equation like x^3 + 5x = 7x^2 - 5 by graphing and reflects on graphing techniques from prior lessons.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
8.7 d2 a
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
11.6 notes b
The document provides instructions for students to complete homework questions, check their answers to a previous worksheet with a partner, and work with partners on new problems involving theorems about segment relationships in circles. Students are assigned one problem to present to the class, with the goal of serving as clear notes examples from the lesson. They are to fill out a graphic organizer in their notes summarizing the three theorems covered.
11.6 notes
The document provides instructions for students to complete homework questions and check their answers to a previous worksheet with a partner. It then explains three theorems about relationships between chords, secants, and tangents in circles. Students are instructed to work with partners on applying the theorems by presenting an example problem to the class, ensuring they show all work and explanations clearly. The document concludes by having students complete a graphic organizer summarizing the three theorems.
8.3 notes a
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
More from mbetzel (20)
7 3 Zero Product Property A
- 1. Opener: Solve each of the 1. 5+x = 5 2. 5x=0 following for x. 3. 11x + 2 = 2 4. x(x‐5)= 0 1
- 2. Homework Questions: 2
- 3. 7.3 The Zero Product Property Topic One: What values of x make the following expression equal to Redefining ZPP zero? x2+5x+6 What values of x make the following expression equal to zero? (x+2)(x+3) What is true about these two expressions? Which form made it easier to find the values of x that make the expression equal to zero? 3
- 4. Topic One: The product of two numbers is zero if and only if one or Redefining ZPP both of the numbers is zero. If a and b are numbers, then .... Solve for x in each of the following. (Ex. 1) 3x (5x ‐ 2)= 0 (Ex. 2) (2x‐8)(5x +3) = 0 It's Your Turn!!! (Ex. 3) ‐2(3x+7) = 0 (Ex. 4) (x+5)(6x+1)=0 4
- 5. Topic One: Redefining ZPP What's wrong here??? Discuss the following Mandy and Billy need to find all the solutions to the equation with your partner. (x+7)(x+11)=77. Mandy says, "I can break up the equation into two simpler ones: (x+7)(x+11)=77 ⇒x+7 = 77 or x+11=77. So there are two answers, x=70 or x=66." Billy replies, " I think you're wrong. I think the solution is x= 0." Who is correct? How do you know he/she is? What is wrong with the other person's answer? 5
- 6. Topic Two: To factor an expression means to write it as the product Factoring with the of two or more expressions. GCF Factor each of the following using GCF. (Ex. 5) 16x2 +8x (Ex. 6) 5x3y2 + 15xy 6
- 7. Topic Three: Factor the following. Then, use ZPP to find solutions for Using Factoring with x. ZPP (Ex. 7) x3 ‐ 9x=0 (Ex. 8) x3=25x Let's get Nspired! Graph f(x)=x3 ‐ 25x. Where does the graph cross the x‐ axis? Do you see any correlation between this and our answer to #6? 7
- 8. Exit Slip: Factor each equation. Then use ZPP to find the solutions to each equation. 1.) 3x2=9x 2.) x2+7x=0 8
- 9. 9