Review question

# When is $x^2 +1$ a factor of $(3+x^4)^n-(x^2+3)^n(x^2-1)^n$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7243

## Suggestion

Let $n$ be a positive integer. Then $x^2 +1$ is a factor of

$(3+x^4)^n-(x^2+3)^n(x^2-1)^n$

for

1. all $n$;

2. even $n$;

3. odd $n$;

4. $n \geq 3$;

5. no values of $n$.

What ideas can we use if we know $x^2+1$ is a factor?

What is the same and what is different about this question compared to other polynomial factorisation questions?