How do you factor 8w^7+18w^6-18w^58w7+18w618w5?

1 Answer
Aug 4, 2016

2w^5(4w - 3)(w + 3)2w5(4w3)(w+3)

Explanation:

f(w) = 2w^5y = 2w^5(4w^2 + 9w - 9)f(w)=2w5y=2w5(4w2+9w9)
Factor y by the new AC Method (Socratic Search)
y = 4w^2 + 9w - 9 = (w + p)(w + q)y=4w2+9w9=(w+p)(w+q)
Converted trinomial y' = w^2 + 9w - 36 = (x + p')(x + q').
p' and q' have opposite signs because ac < 0. Compose factor pairs of (ac = -36)-->...(-3, 12). This sum is 9 = b. Then p' = -3 and q' = 12.
Back to trinomial y, p = (p')/a = -3/4 and q = (q')/a = 12/4 = 3
Factored form of y:
y = (w - 3/4)(w + 3) = (4w - 3)(w + 3)
Factored form of f(w):
f(w) = 2w^5(4w - 3)(w + 3)