9-2

=**9-2 FACTORING GREATEST COMM****ON FACTOR** = = = = To multiply polynomials you can use the distributive property or you can use an area model. In the diagram you can see the product of 2x and (3x+1). = = Example: = 4x^3 + 12x^2 -8x List the Prime factors of each term. 4x^3=2*2*x*x*x Find the factors that all of the terms have in common. 12x^2=2*2*3*x*x 8x=2*2*2*x If your going to factor a polynomial completely, you must factor until there is no common factors other than one. Simplify -4y^2(5y^4 - 3y^2 + 2) -4y^2(5y^4 - 3y^2 + 2) Use the Distributive Property. = -4y^2 (5y^4) - 4y^2 (-3y^2) - 4y^2 (2) Find the product of the coefficients and the sum of the powers with the same base. = -20y^6 + 12y^4 - 8y^2 Simplify. Factor 3x^3 - 12x^2 + 15x **Step 1:** Find the GCF **Step 2:** Factor out the GCF 3x^3 = 3*x*x*x 3x^3 - 12x^2 + 15x 12x^2 = 2*2*3*x*x = 3x (x^2) + 3x (-4x) + 3x (5) 15x = 3*5*x = 3x (x^2 - 4x + 5) The GCF is 3x.
 * x^2 || x^2 || x^2 || x ||
 * x^2 || x^2 || x^2 || x ||
 * Finding the Greatest Common Factor **
 * Multiplying a Monomial and a Trinomial **
 * Factoring Out a Monomial **

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