Question

how would I solve this?

Answer 1

$factor \ x^5-81x$ 

$The \ Greatest \ Common \ Factor \ (GCF) \ is \ x$ 

$Factor \ out \ the \ GCF$ 

$x( \dfrac{x^5}{x} + \dfrac{-18x}{x})$ 

$x(x^4-81)$ $Simplify \ each \ term \ in \ parentheses$ 

$Rewrite \ it \ where \ a=x^2 \ and \ b=9$ 

$x((x^2)2-9^2)$ 

$Use \ Difference \ of \ Squares : a^2-b^2=(a+b)(a-b)$ 

$x(x^2+9)(x^2-9)$ 

$Rewrite \ it \ where \ a=x \ and \ b=3$ 

$x(x^2+9)(x^2-3^2)$ 

$Use \ Difference \ of \ Squares : a^2-b^2=(a+b)(a-b)$ 

$x(x^2+9)(x+3)(x-3)$