When factoring polynomials, we can use a system:

Common?

Difference of squares (2 terms)

Pattern ( x #) (3 terms)

Easy

Ugly

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using these steps we can factor each type of polynomial to its simplest form.

for example:

3y(y+2) – 9(y+2)

because this polynomial has a common factor, y+2, we can substitute it for an unknown variable such as “a”

3ya – 9a

doesn’t that look better?

now we can use the D to find the difference of squares because there’s 2 terms. If there are more than two terms you can skip the D and go right to P.

3a is common on both terms so we simplify polynomial to

3a(y-3)

now we substitute our y+2 back for “a”.

3(y+2)(y-3)

and you’re done! this polynomial cannot be simplified farther.

For a polynomial with 3 terms, you will not use the D, but skip right to P depending on whether you have or will decide if you use the E or the U.