How do you factor x^4-5x^2+4?

Answer 1

Solution:

x⁴ -5x² +4

(x²-4)(x²-1)

(x+2)(x-2)(x+1)(x-1)

Explanation:

In order to factor a trinomial, we find two numbers whose product is ac and whose sum is b.

In the case of x⁴ -5x² +4, these numbers would be -4 and -1. We use x² for each factor in order to account for the x⁴ and -5x². A this point, we notice that x²-4 is a difference of squares that factors to (x+2)(x-2) and x²-1 is also a difference of squares that factors to (x+1)(x-1). So our final answer in factored form is (x+2)(x-2)(x+1)(x-1).

Answer 2

x⁴ - 5x² + 4

(x² - 1)(x² - 4)

(x + 1)(x - 1)(x + 2)(x - 2)