Review question

When is $n^2 x^{2n+3} - 25n x^{n+1} + 150x^7$ divisible by $x^2-1$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7036

Suggestion

The polynomial

$n^2 x^{2n+3} - 25n x^{n+1} + 150x^7$

has $x^2 - 1$ as a factor

1. for no values of $n$,

2. for $n=10$ only,

3. for $n=15$ only,

4. for $n=10$ and $n=15$ only.

Given that $x^2-1$ is a factor, what linear factors of the polynomial do we know?

Can we now use the factor theorem on the polynomial twice?

We may need to be more careful with one factor than the other…