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)