Factoring
• Factoring- 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 6.
• +3
• 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: 12x3-9x2-15x
• 3x is the common factor
• 3x( )
• 3x(4x2 )
• 3x (4x2-3x )
• 3x(4x2-3x-5)
• Check
• 3x(4x2-3x-5)=12x3-9x2-15x