Polynomials 6.13 Zero Product Property.notebook

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Title Page

Factoring Using Distributive Property• I can solve quadratic equations of the form ax2 + bx = 0.

TEKs10.E ­ Factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two

Warm Up

2a

Factor

1. 9x2 + 36x

3. 24m2 np2 +36m2 n2 p

2. 16xz­ 40xz2

4. 5y2 ­15y +4y ­12answer

Polynomials

Homework Answers

Practice Answers1. 18y22. –6q23. 8a24. 3(4x – 3)5. 18(s2 + 3)6. 6(2n2 – 6n + 3)7. –28x(2x – 1)8. –6c(c – 2)9. x(1 – x)10. 3m2, 4

11. 2w2, –712. r2, –913. 7x2, –214. (4 j2 + 5)(2 j + 1)15. (2m2 + 9)(m + 4)16. (6r2 + 7)(3r – 2)17. (9n2 – 2)(4n – 3)18. (11b2 – 6)(10b + 7)19. (8d2 – 3)(8d – 5)20. 4x2 (9π – 4)21. In the first step, the GCF is 8x, not 4x.

Maintain Your Skills

1. B2. B

Practice Worksheet

Math Humor

What did the zero say to the eight?

Math Humor

Nice Belt!

Introduction

What is. . .

What can we say about two numbers when their product equals zero?

What can we say about two numbers when their product equals zero?

­6 x 0 (45)0

46,342 * 00 a12432a2b3c5(0) =

Polynomials 6.13 Zero Product Property.notebook

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Notes

________ Zero Product Property

1. What is the Zero product property?

• If the product of two numbers is zero

• then at least one of the numbers is zero

Date

Notes

2. How to factor a polynomial?

• Find GCF of coefficients

• Find GCF of each variable

• recognize binomials that are additive inverses

(y-7) + (7-y)(y-7) + -1(y-7)

These are the same!

Notes

3. How to solve polynomials?

• completely factor polynomial

• set each factor equal to zero

• solve for the variable

• check the solution set

Find a Friend

Find a friend and tell them how to solve a polynomial.

Would You Rather?

Only eat food that is "fun­sized"...

super­sized?

Examples

1. Solve, then check the solution

Examples

(d­5)(2d+4) = 0

the solution set is 5, ­2

answer(5­5)(2(5)+4) = 0(0)(14) = 0

(5+2)(2(­2)+4) = 0(10)(0) = 0

Polynomials 6.13 Zero Product Property.notebook

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Examples

the solution set is ­5,­3

answer

(­5+3)(­5+5)=0(­2)(0) = 0

(­3+3)(­3+5)=0(0)(2) = 0

(x + 3)(x + 5) = 02. Solve, then check the solution

Examples

the solution set is 0,7

answer

(02)=(7x0)

(72)=(7x7)

x2 ­ 7x = 0x(x ­ 7) = 0x = 0; x = 7

x2 = 7x3. Factor, solve, then check the solution

Examples

the solution set is ­1/3, 1/2 answer 6c(1­2c) + 2(1­2c)

(6c+2) (1­2c)

6c+2=0 1­2c=0c = ­1/3 ­2c=­1c = 1/2

6c ­ 12c2 + 2 ­ 4c = 04. Factor by grouping and solve

Geometry

r

GeometryWrite an expression in factored form for the area of the shaded region.

answer Sides = 2r; Area = 2r x 2r or 4r 2Circle = r 2 (4r2 ­ r2)

r2 (4 ­ )

Application

ApplicationA rocket is shot up in the air at a rate of 32 feet per second. The formula used to measure height is given. How long is the rocket in the air before falling back to the ground?

h = 32t ­ 16t2

answerHeight is 0 feet because it starts at ground level Solve for t

0 = 16t(2­t)0 = 16t 0 = 2 ­ t0 = t t = 22 seconds

Activity

Touch the frog and solve the equation!

Polynomials 6.13 Zero Product Property.notebook

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Homework

PracticeZero Product Property

Worksheet

Closing Questions

Closing QuestionsWhat property states that if the answer is zero, one of the factors must be zero?

Is (4x-4) in completed factored form?

(zero product property)

(no, divisible by 2)