Question

Factorize:
3x³ − x² − 10x

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ 3x^3-x^2-10x=x(3x^2-x-10) \end{gathered}$$
We have to split ($-$1) into two numbers such that their sum is ($-$1) and their product is ($-$30), i.e., $3\times \left(-10\right)$.
Clearly, $\left(-6\right)+5=-1\mathrm{and}\left(-6\right)\times 5=-30$.

$$\begin{gathered} \therefore 3x^3-x^2-10x=x\left(3x^2-x-10\right) \\ =x\left(3x^2-6x+5x-10\right) \\ =x\left[3x(x-2)+5(x-2)\right] \\ =x(x-2)(3x+5) \end{gathered}$$