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. 4x2and 18x 6. 8y5, 30y6II.Factoring out a GCF (Reverse of Distribution) EXAMPLE: 3x(4x5+ 3) multiplies out to ____________ 12x6+ 9x factorsto ____________________ Factoring focuses on undoing multiplication. We are dividing out the GCF. Try factoring out the GCF of these polynomials: 1.4x2+ 24x32. 9 - 9a 3. 2420xx2.8x+12y 5. 14y2+21 6. c dc d2437. 4432221236m nm nm 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. 2339ss4. 2416xV.Think about it…1.Can you use the Zero-Product Property on (x –2)(x –2) = 5? Why or why not? x2.Are x = 4 and x = –6 solutions to (x + 4)(x –6) = 0? Explain. 3.At a movie theatre, which arm rest is yours?