CHAPTER 9 LESSON 4 SOLVE POLYNOMIAL EQUATIONS in FACTORED FORM.

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Presentation transcript:

CHAPTER 9 LESSON 4 SOLVE POLYNOMIAL EQUATIONS in FACTORED FORM

EU/BIG IDEA SOLVE POLYNOMIAL EQUATIONS IN FACTORED FORM

ZERO PRODUCT PROPERTY ZPP Let a and b be real numbers. If ab = 0, then a = 0 or b = 0

Use the zero-product property EXAMPLE 1 Solve (x – 4)(x + 2) = 0. (x – 4)(x + 2) = 0 Write original equation. x – 4 = 0 x = 4 Zero-product property Solve for x. ANSWER The solutions of the equation are 4 and –2. or x + 2 = 0 x = – 2

Use the zero-product property EXAMPLE 1 CHECK Substitute each solution into the original equation to check. (4  4)(4 + 2) = 0 0  6 = 0 0 = 0 ? ? (  2  4)(  2 + 2) = 0  6  0 = 0 0 = 0 ? ?

GUIDED PRACTICE for Example 1 1. Solve the equation (x – 5)(x – 1) = 0. ANSWER The solutions of the equation are 5 and 1.

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

EXAMPLE 2 Find the greatest common monomial factor b.The GCF of 4 and 24 is 4. The GCF of x 4 and x 3 is x 3. So, the greatest common monomial factor of the terms is 4x 3. ANSWER 4x x 3 = 4x 3 (x + 6) SOLUTION Factor out the greatest common monomial factor. b. 4x x 3

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

EXAMP LE 3 Solve an equation by factoring Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of the equation are 0 and – 4. Solve for x. Zero-product property Factor left side. Write original equation.

EXAMP LE 4 Solve an equation by factoring Solve 6n 2 = 15n. 6n 2 – 15n = 0 3n(2n – 5) = 0 3n = 0 n = 0 2n – 5 = 0 n = 5 2 or Solve for n. Zero-product property Factor left side. Subtract 15n from each side. ANSWER The solutions of the equation are 0 and 5/2.

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. ANSWER 0 and – 5 3. a 2 + 5a = s 2 – 9s = 0 ANSWER 0 and x 2 = 2x. ANSWER 0 and

I CAN NOW…. USE THE ZERO PRODUCT PROPERTY (ZPP) TO SOLVE POLYNOMIAL EQUATIONS FACTOR POLYNOMIALS SO THAT I CAN USE FACTORING TO SOLVE POLYNOMIAL EQUATIONS

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