Question

Divide $p\left(x\right)=x^4-a^4$ by $x-a$.

Answer 1

Given the polynomial, $p\left(x\right)=x^4-a^4$ and the binomial $x-a$,

We have to divide $p\left(x\right)$ by $x-a$.

$\therefore \frac{x^4-a^4}{x-a}$

$=\frac{{\left(x^2\right)}^2-{\left(a^2\right)}^2}{x-a}$

$=\frac{(x^2-a^2)(x^2+a^2)}{x-a}$

$=\frac{(x-a)(x+a)(x^2+a^2)}{x-a}$

$=(x+a)(x^2+a^2)$.