Factoring FactoringFactoring- to factor an algebraic expression we change the form of an expression and put it in factored form. It is the reverse of using the distributive rule. Example: 2(x+3) is an expression in factored form. The first factor is 2. The second factor is (x+3).

Factoring Let’s use the distributive rule with this expression 2(x+3) =2x+6 When we factor we start with the expression 2x+6 and find it factors. The 2 and the (x+3) are factors of 2x+6.

Factoring Let’s factor this expression: 2x+6 Look for a common factor of both terms in the expression 2x+6. 2 is a factor of 2x and of 6 so “2” is a common factor of both terms.

Factoring 2(x+3)=2x+6 When using the distributive rule we multiply and eliminate the parenthesis. When we factor we are doing the reverse process so we create parentheses. When we look at the expression 2x+6 we see that 2 is a common factor of both terms. Put the common factor of 2 outside the parenthesis. 2( ) To find out the expression that goes inside the parenthesis: Ask yourself: What do I multiply 2 by to get 2x or divide 2 into 2x and get: x 2(x ) For the second term in the parenthesis what do you multiply 2 by to get 6 or divide 2 into In factored form the result is: 2(x+3) Check the results by multiplying back to get the original expression. 2(x+3)=2x+6

Factoring Examples: Factor: 6x-12 6 is the common factor 6( ) 6 (x ) 6(x-2) Check 6(x-2)= 6x-12

Factoring Examples: Factor: -4x-12y+20z 4 is the common factor 4( ) 4(-x ) 4 (-x-3y ) 4(-x-3y+5z) Check 4(-x-3y+5z)=-4x-12y+20z

Factoring Examples: Factor: 12x 3 -9x 2 -15x 3x is the common factor 3x( ) 3x(4x 2 ) 3x (4x 2 -3x ) 3x(4x 2 -3x-5) Check 3x(4x 2 -3x-5)=12x 3 -9x 2 -15x