Question

Select the factored form of the expression if it cannot be factored select already in factored form n^2+16n-64

Answer 1

Consider the expression $n^2+16n-64.$

Since

$D=b^2-4ac=16^2-4\cdot (-64)=256+256=512,\\ \\\sqrt{D}=16\sqrt{2},$

then

$n_1=\dfrac{-16+16\sqrt{2}}{2}=-8+8\sqrt{2},\ n_2=\dfrac{-16-16\sqrt{2}}{2}=-8-8\sqrt{2}.$

Therefore, the factored form of  $n^2+16n-64$ is $(n+8-8\sqrt{2})(n+8+8\sqrt{2}).$