This week we learned a technique/acronym to factor polynomial expressions

CDPEU

Can Divers Pee Easily Underwater

Common Factor, Difference of squares, Pattern, Easy, Ugly

C – Check if there is a common factor

D – Check if there is a difference of squares

P – Check if there is a pattern, is it x^2, x, then a number or x^10, x^5, then a number

E – Check if the leading coefficient is 1 and is 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. Look for the GCF, Checking for a common factor and removing it is the first step. Take that factor out and place it at the front of the bracket.

For example: 3x^2 + 9x^2 – 30

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

3(x^2 + 3x^2 – 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.

z^2 – 1

(z+1)(z-1)

If it is a trinomial expression, ax^2 + 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.

x^2 + 7x + 10

(x + 2)(x + 5)

2 + 5 = 9

2 x 5 = 20

If a does not = 1 we can use the different methods we were taught in class of which are the guess and test method or area diagram.