Question

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

Answer 1

\[\text{ To factorise }y^2 + 5y - 36,\text{ we will find two numbers p and q such that }p + q = 5\text{ and }pq = - 36 . \]
Now, 
\[9 + ( - 4) = 5 \]
and 
\[9 \times ( - 4) = - 36\]
\[\text{ Splitting the middle term 5y in the given quadratic as } - 4y + 9y, \text{ we get: }\]
\[ y^2 + 5y - 36 = y^2 - 4y + 9y - 36\]
\[ = ( y^2 - 4y) + (9y - 36)\]
\[ = y(y - 4) + 9(y - 4)\]
\[ = (y + 9)(y - 4)\]