9.4 Notes- GCF and ZPP Key - 9.4 Solving Polynomial Equations in Factored Form I The Greatest Common Factor A GCF or Greatest Common Factor is the

9.4 Notes- GCF and ZPP Key - 9.4 Solving Polynomial...

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9.4 - Solving Polynomial Equations in Factored Form I. The Greatest Common Factor A GCF, or Greatest Common Factor, is the largest monomial that divides evenly into each term of a polynomial. Let’s start by finding the GCF of the following numbers and monomials: 1. 3 and 9 2. 2 and 11 3. 12 and 24 4. 8x and 20x 5. 4x 2 and 18x 6. 8y 5 , 30y 6 II. Factoring out a GCF (Reverse of Distribution) EXAMPLE: 3x(4x 5 + 3) multiplies out to ____________ 12x 6 + 9x factors to ____________________ Factoring focuses on undoing multiplication. We are dividing out the GCF. Try factoring out the GCF of these polynomials: 1. 4x 2 + 24x 3 2. 9 - 9a 3. 2 4 20 x x 2. 8x+12y 5. 14y 2 +21 6. c d c d 2 4 3 7. 4 4 3 2 2 2 12 3 6 m n m n m n
III.The Zero-Product Property Recall the two different forms of polynomials, standard form and factored form. Standard Form: 2x2+ 7x 15 = 0 Factored Form: (2x 3)(x + 5) = 0 How can we solve for x in the following equations in factored form? a)(x 3)(x + 2) = 0 b) (x + 1)(x + 3) = 0 These x values are called ___________________________________________________________________. This property is called the Zero-Product Property. To use the ZPP, the polynomial must be in factored form and the equation must equal zero. Let’s Practice: 1) (2x + 3)(x 4) = 0 2) 6x(x 4) = 0 The Zero-Product Property: If ab= 0, then _______________________.
3) (2x + 1)(3x 3)(x 5) = 0 4) x(y 8)(2y 9) = 0 IV.Try it! Factor and solve. 1.228xx2. 2615n n
3. 2339ss4. 2416xV.Think about it…1.Can you use the Zero-Product Property on (x 2)(x 2) = 5? Why or why not? x 2.Are x = 4 and x = 6 solutions to (x + 4)(x 6) = 0? Explain. 3.At a movie theatre, which arm rest is yours?

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