When factoring a polynomial, there are a couple of steps to take first when trying to factor it.

Always look for the GCF (greatest common factor) before anything else. Checking for a common factor and removing it is the first step. This GCF is for each monomial or the polynomial. When you take it out, place it in-front of the bracket.

For example: + – 30

The greatest common factor is 3, because they all share the GCF 3.

3( + – 10)

Now, we are either left with a binomial expression or a trinomial expression.

If it is a binomial expression, check to see if there is a difference of squares. Factor as such.

– 1

(z+1)(z-1)

If it is a trinomial expression, + bx + c, a either = 1 or does not equal 1.

If a, or the leading coefficient, is a negative number, factor out the negative first.

If a = 1, we can use the method of inspection, finding two numbers that have the sum of the middle term and the product of the last term.

+ 9x + 20

(x + 4)(x + 5)

4 + 5 = 9

4 x 5 = 20

If a does not = 1 and is higher or lower, we can use the method of guess and test or area diagram.

Then check if there is possibility for further factoring, checking to see if there is a difference of squares that can be factored.

We can use an acronym to remember all the steps when factoring polynomials.

CDPEU

Can Divers Pee Easily Underwater

Common factor Difference of squares Pattern Easy Ugly

C – look to see if there is a common factor

D – look to see if there is a difference of squares to factor

P – is it , x, then a number or , , then a number

E – is the leading coefficient 1 and easy to factor by finding two terms that have the sum of the middle term and product of the last.

U – is it an ugly expression that takes more work to find the factoring

Then always check if there is possible further factoring.