Question

Factorise:
$a^2+5a-104$

Answer 1

In the given polynomial $a^2+5a-104$,

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

The middle term is $5a$ and its coefficient is $5$.

The last term is a constant term $-104$.

Multiply the coefficient of the first term by the constant $1\times -104=-104$.

We now find the factor of $-104$ whose sum equals the coefficient of the middle term, which is $5$ and then factorize the polynomial $a^2+5a-104$ as shown below:

$a^2+5a-104=a^2+13a-8a-104=a(a+13)-8(a+13)=(a-8)(a+13)$

Hence, $a^2+5a-104=(a-8)(a+13)$.