Can someone help me factor:

Question

4u^3+3u^2-9u+2

I don’t understand how to factor 4 terms problems.

Answer 1

let f(u) = 4u^3+3u^2-9u+2
f(1) = 4 + 3 - 9 + 2 = 0
so u-1 is a factor.
Using synthetic division, or your other favourite method that was taught to you,
4u^3+3u^2-9u+2 = (u-1)(4u^2 + 7u - 2)
= (u-1)(u+2)(4u - 1)

4u^3+3u^2-9u+2 = 0
(u-1)(u+2)(4u - 1) = 0
u = 1,-2,1/4