Chapter 5.3, Problem 16E

To determine

what is wrong in the factor of the polynomial $3k^3-12k^2-15k$.

First factor out $3k$ ,

$3k^3-12k^2-15k=3k\left(k^2-4k-5\right)$

After that given factored form is,

$\begin{array}{c}{k}^2-4k-5=k^2-5k+k-5\\ =k\left(k-5\right)+\left(k-5\right)\\ =\left(k-5\right)\left(k+1\right)\end{array}$

The answer of the student is $\left(k-5\right)\left(k+1\right)$.

And what will be the correct factored form of the polynomial $3k^3-12k^2-15k$.