This week in pre-calc 11, I learned how to factor polynomial expressions. C D P E U are the 5 steps to factoring a polynomial.

C = Common, D = Difference of squares, P = Pattern, E = Easy pattern, U = Ugly pattern

Common means finding a number or variable that can factor out from a binomial or a trinomial.

Ex. 64x + 16

= 16 (4x + 1)

 

Difference of squares is only used in binomials. The sign in between the expression has to be negative (-) and one number or variable has to be squared.

Ex. 25x²– 9

= (5x – 3)(5x + 3)

 

Pattern is to check if it’s a trinomial following the expression “(a)x² + bx + c”.

– Easy patterns are when there is no coefficient in front of the x². I then factor out to find the product of c and the sum of b with the same numbers.

Ex. x² + 8x + 12

= (x + 6)(x+ 2)

– Ugly patterns are when there is a coefficient in front of the x². My method is to multiply the coefficient into the term without a variable. It then becomes an easy pattern, then I factor it out. Once I get an answer with the easy pattern, I divide both sides by the coefficient of x².

Ex. 2x² + 3x – 2

= x² + 3x – 4

= (x + 4)(x – 1)

= (x + )(x – )

= (x + 2)(2x – 1)