Factorize each of the following algebraic expression:
Question:

Factorize each of the following algebraic expression:
y2 + 5y − 36

Solution:

To factorise $y^{2}+5 y-36$, we will find two numbers $p$ and $q$ such that $p+q=5$ and $p q=-36$.

Now,

$9+(-4)=5$

and

$9 \times(-4)=-36$

Splitting the middle term 5y in the given quadratic as $-4 y+9 y$, we get:

$\mathrm{y}^{2}+5 \mathrm{y}-36=\mathrm{y}^{2}-4 \mathrm{y}+9 \mathrm{y}-36$

$=\left(y^{2}-4 y\right)+(9 y-36)$

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

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

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