Question

Factorize:
3x² − 14x + 8

Answer 1

We have:
$3x^2-14x+8$
We have to split ($-$14) into two numbers such that their sum is ($-$14) and their product is 24, i.e., $3\times 8$.
Clearly, $\left(-12\right)+\left(-2\right)=-14\mathrm{and}\left(-12\right)\times \left(-2\right)=24$.

$$\begin{gathered} \therefore 3x^2-14x+8=3x^2-12x-2x+8 \\ =3x\left(x-4\right)-2\left(x-4\right) \\ =\left(x-4\right)\left(3x-2\right) \end{gathered}$$