Week 5 – Factoring Polynomial Expressions

This week in pre-calc 11, we learned how to factor polynomial expressions. There are 5 steps you can use to factor a polynomial, CDPEU. CDPEU stands for Common, Difference of squares, Pattern, Easy pattern and Ugly pattern.

Common means finding any like terms in the expression and combining them together

Difference of squares is used in binomials only (2 term expression) and there must be a — sign because it’s a difference. Difference of squares only works if everything is a perfect square. When factoring a difference of squares, they will always be conjugates so there is no middle term

Ex.64 $x^2$

64 $x^2$ = 8x x 8x

25 = 5×5

(8x+5)(8x-5) = 64 $x^2$

Pattern, Easy pattern and Ugly patterns are used for trinomials only (expression with 3 terms)

Pattern is figuring out if the expression is an easy pattern or an ugly pattern.

Easy pattern $x^2$ +6x+8 it’s simple because there is no coefficient in the first term and you find 2 numbers that add to the middle term and multiply to the term.

Ex. $x^2$ +6x+8

8 = 1×8, 2×4 2+4 = 6

(x+2)(x+4) = $x^2$ +6x+8

Ugly pattern is $6x^2$ +11x-10 an ugly pattern is ugly because there is a coefficient with the first term. An easy way to factor an ugly pattern is using a box

Some expressions do not factor.

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