09-2+Factoring+Using+the+Distributive+Property

  = = **9-2 Factoring Using the Distributive Property ** 

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Factoring Using the Distributive Property is the opposite process of using the Distributive Property to multiply a polynomial by a monomial. We use this process to express a polynomial as the product of a monomial factor and a polynomial factor. **Factoring** a polynomial means to find its completely factored form. ====== 

//Example 1 //

 * Use the Distributive Property to factor each polynomial

**

Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF.

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 12a² + 16a = 4a(3 x a) + 4a( 2 x 2) Rewrite each term using the GCF  ======

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 = 4a(3a) + 4a(4) Simplify remaining factors  ======

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 = 4a(3a +4) <span style="color: rgb(0, 0, 255); font-family: Arial,Helvetica,sans-serif;">Distribute <span style="color: rgb(0, 0, 0); font-family: Arial,Helvetica,sans-serif;"> ======

<span style="color: rgb(0, 0, 0); font-family: Arial,Helvetica,sans-serif;">
<span style="color: rgb(0, 0, 0); font-family: Arial,Helvetica,sans-serif;"> The Distributive Property can also be used to factor some polynomials having four or more terms. This method is called **factoring by grouping** because pairs of terms are grouped together and then factored. The Distributive Property is then applied the second time to factor a common binomial factor.

<span style="color: rgb(0, 0, 0); font-family: Arial,Helvetica,sans-serif;">
<span style="color: rgb(0, 0, 0); font-family: Arial,Helvetica,sans-serif;">**Factor 4//ab// + 8//b// + 3//a// + 6**

//Example 3//
//**Solve an equation by Factoring**//


 * Solve x²=7x. Then check the solution.**

Write the equation so that it is of the form ab = 0

x = 7 <span style="color: rgb(0, 0, 255);">Solve each equation.
The solution set is {0, 7}. <span style="color: rgb(0, 0, 255);">Check by substituting 0 and 7 for x in the original equation.

Link 1 [|Factoring Distibutive Properties]

Link 2 [|Factoring using distributive properties]