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.

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

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

= 4a(3a +4) Distribute

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.

Example 2

Factor 4ab + 8b + 3a + 6

4ab + 8b + 3a + 6

= (4ab + 8b) + (3a + 6) Group terms with common factors

= 4b(a + 2) + 3 (a + 2) Factor the GCF from each grouping

= (a + 2)(4b + 3) Distributive Property

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

x²=7x Original equation

x² - 7x = 0 Subtract 7x from each side.

x (x - 7) = 0 Factor the GCF of x2 and -7, witch is x.

x = 0 or x - 7 = 0 Zero Product Property

x = 7 Solve each equation.

The solution set is {0, 7}. Check by substituting 0 and 7 for x in the original equation.

9-2 Factoring Using the Distributive Property## 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.

Factoringa polynomial means to find its completely factored form.Example 1Use 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.

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

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

## = 4a(3a +4) Distribute

The Distributive Property can also be used to factor some polynomials having four or more terms. This method is called

factoring by groupingbecause pairs of terms are grouped together and then factored. The Distributive Property is then applied the second time to factor a common binomial factor.Example 2Factor 4ab+ 8b+ 3a+ 6## 4ab + 8b + 3a + 6

## = (4ab + 8b) + (3a + 6) Group terms with common factors

## = 4b(a + 2) + 3 (a + 2) Factor the GCF from each grouping

## = (a + 2)(4b + 3) Distributive Property

Example 3Solve an equation by FactoringSolve x²=7x. Then check the solution.Write the equation so that it is of the form ab = 0

## x²=7x Original equation

## x² - 7x = 0 Subtract 7x from each side.

## x (x - 7) = 0 Factor the GCF of x2 and -7, witch is x.

## x = 0 or x - 7 = 0 Zero Product Property

## x = 7 Solve each equation.

The solution set is {0, 7}. Check by substituting 0 and 7 for x in the original equation.

Link 1

Factoring Distibutive Properties

Link 2

Factoring using distributive properties