How do you solve 4x^3 + x^2 - 4x - 1=0 by factoring?

1 Answer
May 21, 2018

(x - 1)(x+1)(4x+1) = 0
x = 1 , -1 , -1/4

Explanation:

4x^3 + x^2 - 4x - 1 = 0

Start of Factoring by Grouping:
(4x^3 + x^2) + (-4x - 1) = 0
x^2(4x + 1) - 1(4x + 1) = 0
(x^2 - 1)(4x + 1) = 0

We still have a Difference of Squares (x^2 - a^2) = (x-a)(x+a)
(x - 1)(x+1)(4x+1) = 0

Set each Factor equal to 0 and Solve for x:
x - 1 = 0 -> x = 1
x + 1 = 0 -> x = -1
4x + 1 = 0 -> x = -1/4