Question

Factor completely: 2x3 + 14x2 + 4x + 28

Answer 1

first 2 is a factor:
= 2(x^3 + 7x^2 + 2x + 14)
use factor theorem
:- this is a tedious one
f(-7) = 0 so (x+ 7) is a factor

Answer 2

First, factor out the 2: 2(x^3+7x^2+2x+14)
Then, divide the polynomial in the parentheses by one of its factors (x+7), which you can find by plugging in one of the factors of the last number of the polynomial until you get 0. So when you plug -7 into the polynomial, you get 0. So then divide it by x+ the opposite of 7 which is +7 (x+7):
____________________
x+7|x^3+7x^2+2x+14 = x^2+2

So: x^3+7x^2+2x+14 = (x^2+2)(x+7)
And that factors to: 2(x+2)(x+2)(x+7)