Question

Factorise:
$a^2+12a+32$

Answer 1

In the given polynomial $a^2+12a+32$,

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

The middle term is $12a$ and its coefficient is $12$.

The last term is a constant term $32$.

Multiply the coefficient of the first term by the constant $1\times 32=32$.

We now find the factor of $32$ whose sum equals the coefficient of the middle term, which is $12$ and then factorize the polynomial $a^2+12a+32$ as shown below:

$a^2+12a+32=a^2+4a+8a+32=a(a+4)+8(a+4)=(a+4)(a+8)$

Hence, $a^2+12a+32=(a+4)(a+8)$.