Question

Factorize:
y² − 4y + 3

Answer 1

We have:
$y^2-4y+3$
We have to split ($-$4) into two numbers such that their sum is ($-$4) and their product is 3.
Clearly, $\left(-3\right)+\left(-1\right)=-4\mathrm{and}\left(-3\right)\times \left(-1\right)=3$.

$$\begin{gathered} \therefore y^2-4y+3=y^2-3y-y+3 \\ =y(y-3)-1(y-3) \\ =(y-3)(y-1) \end{gathered}$$