Question

Which binomial is a factor of x⁴ - 4x² - 4x + 8
1. x-2
2. x+2
3.x-4
4.x+4

Answer 1

The binomial can be factored as (x-2)(x+1). Option 1 is the right choice.

Let's factor the given binomial:

x^4 − 4x^2 −4x+8

Find a common factor

Observe that all the terms in the given binomial have a common factor of 4. Factoring out 4 gives us:

4(x^2 − x − 1)

Factor the remaining trinomial

Now, let's factor the remaining trinomial x^2 − x − 1:

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

Combining the factors, we get the complete factorization:

(x−2)(x^3 + 2x^2 −4)

Option 1 is the right choice.