Question

Show all steps to factor completely: x^4 - 5x + 4.

a) (x^2 - 4)(x^2 - 1)
b) (x^2 - 4)(x^2 + 1)
c) (x^2 - 2)(x^2 - 2)
d) (x^2 - 4x + 4)(x^2 - x - 1)

Answer 1

To factor completely, we need to find the factors of the given expression that can be further factored. By grouping terms and applying the distributive property, we can factorize the expression as (x(x - 1)(x + 1))(x - 2)(x + 2) + 4.

Step-by-step explanation:

To factor the expression completely, we need to find the factors of the given expression that can be further factored. We start by grouping the terms:

x^4 - 5x + 4 = (x^4 - 4x^2) - (x^2 - 4x) + 4

= x^2(x^2 - 4) - x(x^2 - 4) + 4

= (x^2 - x)(x^2 - 4) + 4

= (x(x - 1)(x + 1))(x^2 - 4) + 4

= (x(x - 1)(x + 1))(x - 2)(x + 2) + 4

Therefore, the correct factorization is (x(x - 1)(x + 1))(x - 2)(x + 2) + 4, which is not one of the given options.