Question

what is the simplified form of X to the fourth power -81 over X+3?

Does anyone know the rest of the answers for the quick check?

Answer 1

You have to use the formula

$a^2-b^2 = (a+b)(a-b)$

twice: we have

$x^4-81 = (x^2+9)(x^2-9) = (x^2+9)(x+3)(x-3)$

So, we have

$\dfrac{x^4-81}{x+3} = \dfrac{(x^2+9)(x+3)(x-3)}{x+3} = (x^2+9)(x-3)$