Question

How do you use the factor theorem to determine whether x-2 is a factor of `4x^4 – 15x^2 – 4`?

Answer 1

The expression `x-2` is a factor of `4x^4-15x^2-4`

Explanation:

The factor theorem states that `(x-a)` is a factor of a polynomial `P(x)` if and only if `P(a)=0`

So to check if `(x-2)` is a factor of `4x^4-15x^2-4` we have to find the value of the polynomial for `x=2`

So we have to calculate:

`4*2^4-15*2^2-4=4*16-15*4-4=64-60-4=0`

The value is zero so according to the factor Theorem `x-2` is a factor of `4x^4-15x^2-4`