Question

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

Answer 1

`(3p^2+4)(p+1)`

Explanation:

Note that the ratio of the coefficients of the first two terms `(3:12)`
is equal to the ratio of the coefficients of the last two terms `(4:16)`
(name, in reduced terms: `(1:4)` )

So if we extract the common factor from the first two terms and the common factor from the last two terms:
`color(red)(3p^3+12p^2) + color(blue)(4p+16)`

`=color(red)((3p^2))color(green)((p+1))+color(blue)((4))color(green)((p+1))`

then extract the common factor from each of these terms:
`=color(purple)((3p^2+4))color(green)((p+1))`