Question

Factorise $x^2-3x+2$.

Answer 1

In the given polynomial $x^2-3x+2$,

The first term is $x^2$ and its coefficient is $1$.

The middle term is $-3x$ and its coefficient is $-3$.

The last term is a constant term $2$.

Multiply the coefficient of the first term by the constant $2\times 1=2$.

We now find the factor of $2$ whose sum equals the coefficient of the middle term, which is $-3$ and then factorize the polynomial $x^2-3x+2$ as shown below:

$x^2-3x+2=x^2-x-2x+2=x(x-1)-2(x-1)=(x-1)(x-2)$

Hence, $x^2-3x+2=(x-1)(x-2)$.