Question

Factorise:
$p^2+p-132$

Answer 1

In the given polynomial $p^2+p-132$,

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

The middle term is $p$ and its coefficient is $1$.

The last term is a constant term $-132$.

Multiply the coefficient of the first term by the constant $1\times -132=-132$.

We now find the factor of $-132$ whose sum equals the coefficient of the middle term, which is $1$ and then factorize the polynomial $p^2+p-132$ as shown below:

$p^2+p-132=p^2+12p-11p-132=p(p+12)-11(p+12)=(p-11)(p+12)$

Hence, $p^2+p-132=(p-11)(p+12)$.