Question

Factorise:
$z^2+13z+40$

Answer 1

In the given polynomial $z^2+13z+40$,

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

The middle term is $13z$ and its coefficient is $13$.

The last term is a constant term $40$.

Multiply the coefficient of the first term by the constant $1\times 40=40$.

We now find the factor of $40$ whose sum equals the coefficient of the middle term, which is $13$ and then factorize the polynomial $z^2+13z+40$ as shown below:

$z^2+13z+40=z^2+8z+5z+40=z(z+8)+5(z+8)=(z+5)(z+8)$

Hence, $z^2+13z+40=(z+5)(z+8)$.