factor x^3 + 3x^2 + 3x + 2

Answer 1

x^3 + 3x^2 + 3x + 2

let f(x) = x^3 + 3x^2 + 3x + 2
f(1) = 1+3+3+2 ≠ 0
f(-1) = -1 + 3 - 3 + 2 ≠0
f(2) = ..... ≠ 0
f(-2) = -8 + 12 - 6 + 2 = 0 , so x+2 is a factor
do a long division to get the remaining quadratic factor.