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

Question

1631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-01T10:37:31

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

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 $4x^4-15x^2-4$

How do you use the factor theorem to determine whether x-2 is a factor of 4x^4 – 15x^2 – 44x^4 – 15x^2 – 4?