Question

How do you factor `4b^3 +3b^2-16b-12`?

Answer 1

Regroup to maximize the extractable factors
`4b^3+3b^2-16-12 = color(red)(4b^3-16b) + color(blue)(3b^2-12)`

`=color(red)(4b(b^2-4)) + color(blue)(3(b^2-4))`

`=(4b+3)(b^2-4)`

Recognize the second term as the Difference of Squares
`=(4b+3)(b+2)(b-2)`

Answer 2

Collect `4b` between the first and third term and `+3` between the second and rourth:
`4b(b^2-4)+3(b^2-4)=` collect `(b^2-4)`
`(b^2-4)(4b+3)`