common factors
· Common factors are numbers or variables that can divide a polynomial without leaving any remainders.
· There are five steps to common factor a simple polynomial:
o Find a common factor of the co-efficient and numbers.
o Find a common factor of all variables.
o Put the common factor of the numbers and variables together.
o Divide the entire polynomial with the common factor.
o Put the common factor on the outside of brackets that are around the factored polynomial.
Example: Factor the following polynomial using common factoring.
5x^2 + 10x
Common factor = 5x
= 5x(x + 2)
· Another common factoring scenario is as in a(x+y) + a(x+y) format.
· In this case the common factor is the term on the outside of the bracket or the binomial on the inside of the bracket.
Example: Factor the following polynomial using common factoring.
2x (a + 2) – 4(a+2)
Note: When common factoring a binomial one term must be same.
Common factor = (a+2)
= (a + 2)(2x – 4)
· Common factoring a polynomial with 4 terms is done using grouping. Grouping is collecting that have a factor in common.
Example: Factoring the following using grouping.
ab + ac + xb + xc
= (ab + ac)(+ xb + xc)
= a(b + c) + x(b + c)
= (b + c)( a + x)
· All types of common factoring require the greatest common factor for the polynomial to be factored.
· There are five steps to common factor a simple polynomial:
o Find a common factor of the co-efficient and numbers.
o Find a common factor of all variables.
o Put the common factor of the numbers and variables together.
o Divide the entire polynomial with the common factor.
o Put the common factor on the outside of brackets that are around the factored polynomial.
Example: Factor the following polynomial using common factoring.
5x^2 + 10x
Common factor = 5x
= 5x(x + 2)
· Another common factoring scenario is as in a(x+y) + a(x+y) format.
· In this case the common factor is the term on the outside of the bracket or the binomial on the inside of the bracket.
Example: Factor the following polynomial using common factoring.
2x (a + 2) – 4(a+2)
Note: When common factoring a binomial one term must be same.
Common factor = (a+2)
= (a + 2)(2x – 4)
· Common factoring a polynomial with 4 terms is done using grouping. Grouping is collecting that have a factor in common.
Example: Factoring the following using grouping.
ab + ac + xb + xc
= (ab + ac)(+ xb + xc)
= a(b + c) + x(b + c)
= (b + c)( a + x)
· All types of common factoring require the greatest common factor for the polynomial to be factored.