Question

Factor each completely.
4b^3-28b^2-b+7

Answer 1

in these ideally you wanna pair up your evens and odds

Answer 2

(4b^3 - b) + (-28b + 7)

that way we have a quadratic left over that either factors or not

Answer 3

b ( 4b^2 -1) - 7( 4b^2 - 1)
= (4b^2 -1) ( b - 7)

Answer 4

Factor out a 4b^2 from the first 2 terms and a -1 out of the 2nd 2 terms:
4b^2(b-7)-1(b-7)
=(4b^2-1)(b-7)
You can factor further here, it is a difference of 2 squares:
(2b-1)(2b+1)(b-7)