1 / 16

Unit 6: lesson 8.4 SWBAT solve polynomial equations in factored form & factor the GCF.

Unit 6: lesson 8.4 SWBAT solve polynomial equations in factored form & factor the GCF. Section 8.4 “Solve Polynomial Equations in Factored Form”. Zero-Product Property. If ab = 0, then a = 0 or b = 0.

eclegg
Download Presentation

Unit 6: lesson 8.4 SWBAT solve polynomial equations in factored form & factor the GCF.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit 6: lesson 8.4 SWBAT solve polynomial equations in factored form & factor the GCF.

  2. Section 8.4 “Solve Polynomial Equations in Factored Form” Zero-Product Property If ab = 0, then a = 0 or b = 0. The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors. (x – 4)(x + 2) = 0 The solutions of such an equation are called ROOTS. x + 2 = 0 x – 4 = 0 x = -2 x = 4

  3. Example 1A: Use the Zero Product Property Use the Zero Product Property to solve the equation. Check your answer. (x – 7)(x + 2) = 0 Use the Zero Product Property. x – 7 = 0 or x + 2 = 0 Solve each equation. x = 7 or x = –2 The solutions are 7 and –2.

  4. Example 1B: Use the Zero Product Property Use the Zero Product Property to solve each equation. Check your answer. (x – 2)(x) = 0 (x)(x – 2) = 0 Use the Zero Product Property. x= 0 or x – 2 = 0 Solve the second equation. x = 2 The solutions are 0 and 2.

  5. Use the Zero Product Property to solve the equation. Check your answer. (x + 4)(x – 3) = 0 Use the Zero Product Property. x + 4 = 0 or x – 3 = 0 x = –4 or x = 3 Solve each equation. The solutions are –4 and 3.

  6. Solve the equations (x – 5)(x + 1) = 0 (2x – 3)(4x + 1) = 0

  7. Using the Zero Product Property Solve the equation (x – 1)(x + 7) = 0

  8. You try: Solve the equation (z – 6)(z + 6) = 0.

  9. Try this one: Solve the equation (x – 4)2 = 0

  10. a. The GCF of 12 and 42 is 6. The variables xand yhave no common factor. So, the greatest common monomial factor of the terms is 6. ANSWER 12x + 42y = 6(2x + 7y) Factor out the greatest common monomial factor. a.12x + 42y SOLUTION

  11. b. The GCF of 4 and 24 is 4. The GCF of x4 and x3 is x3. So, the greatest common monomial factor of the terms is 4x3. ANSWER 4x4+ 24x3 = 4x3(x + 6) Factor out the greatest common monomial factor. b. 4x4+ 24x3 SOLUTION

  12. ANSWER 14m+ 35n = 7(2m + 5n) GUIDED PRACTICE 2. Factor out the greatest common monomial factor from 14m + 35n.

  13. ANSWER The solutions of the equation are 0 and – 4. EXAMPLE 3 Solve2x2+ 8x = 0. 2x2+ 8x = 0 Write original equation. 2x(x + 4) = 0 Factor left side. or x + 4 = 0 2x= 0 Zero-product property or x = 0 x =– 4 Solve for x.

  14. 5 5 2 2 n = ANSWER . The solutions of the equation are 0 and Solve 6n2 = 15n. 6n2– 15n = 0 Subtract 15nfrom each side. 3n(2n – 5) =0 Factor left side. or 2n – 5= 0 3n= 0 Zero-product property or n = 0 Solve for n.

  15. 1 1 2 2 ANSWER ANSWER ANSWER 0 and – 5 0 and 3 . 0 and GUIDED PRACTICE Solve the equation. 3. a2+ 5a = 0 5. 4x2 = 2x. 4. 3s2– 9s = 0

More Related