Question

Factorize the following

$y^2+5y-36$

• A. $(y-4)(y+9)$
• B. $(y+4)(y+9)$
• C. $(y-4)(y-9)$
• D. None of these

Answer 1

The correct option is A $(y-4)(y+9)$

In the given polynomial $y^2+5y-36$,

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

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

The last term is a constant term $-36$.

Multiply the coefficient of the first term by the constant $1\times (-36)=-36$.

We now find the factor of $-36$ whose sum equals the coefficient of the middle term, which is $5$ and then factorize the polynomial $y^2+5y-36$ as shown below:

$y^2+5y-36$

$=y^2+9y-4y-36$

$=y(y+9)-4(y+9)$

$=(y+9)(y-4)$

Hence, $y^2+5y-36=(y+9)(y-4)$.