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

Dec 1, 2015

The expression $x - 2$ is a factor of $4 {x}^{4} - 15 {x}^{2} - 4$

#### Explanation:

The factor theorem states that $\left(x - a\right)$ is a factor of a polynomial $P \left(x\right)$ if and only if $P \left(a\right) = 0$

So to check if $\left(x - 2\right)$ is a factor of $4 {x}^{4} - 15 {x}^{2} - 4$ we have to find the value of the polynomial for $x = 2$

So we have to calculate:

$4 \cdot {2}^{4} - 15 \cdot {2}^{2} - 4 = 4 \cdot 16 - 15 \cdot 4 - 4 = 64 - 60 - 4 = 0$

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