Question

Factorize each of the following algebraic expression:
a² + 3a − 88

Answer 1

\[\text{ To factorise }a^2 + 3a - 88,\text{ we will find two numbers p and q such that }p + q = 3\text{ and }pq = - 88 . \]
Now, 
\[11 + ( - 8) = 3 \]
and 
\[11 \times ( - 8) = - 88\]
\[\text{ Splitting the middle term 3a in the given quadratic as }11a - 8a,\text{ we get: }\]
\[ a^2 + 3a - 88 = a^2 + 11a - 8a - 88\]
\[ = ( a^2 + 11a) - (8a + 88)\]
\[ = a(a + 11) - 8(a + 11)\]
\[ = (a - 8)(a + 11)\]