Question

Factorise:
$z^2-7z-30$

Answer 1

In the given polynomial $z^2-7z-30$,

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

The middle term is $-7z$ and its coefficient is $-7$.

The last term is a constant term $-30$.

Multiply the coefficient of the first term by the constant $1\times -30=-30$.

We now find the factor of $-30$ whose sum equals the coefficient of the middle term, which is $-7$ and then factorize the polynomial $z^2-7z-30$ as shown below:

$z^2-7z-30=z^2-10z+3z-30=z(z-10)+3(z-10)=(z-10)(z+3)$

Hence, $z^2-7z-30=(z-10)(z+3)$.