Question

Factorize each of the following algebraic expression:
a² − 14a − 51

Answer 1

\[\text{ To factorise }a^2 - 14a - 51,\text{ we will find two numbers p and q such that }p + q = - 14\text{ and }pq = - 51 . \]
Now, 
\[3 + ( - 17) = - 14 \]
and 
\[3 \times ( - 17) = - 51\]
\[\text{ Splitting the middle term }- 14a\text{ in the given quadratic as }3a - 17a,\text{ we get: }\]
\[ a^2 - 14a - 51 = a^2 + 3a - 17a - 51\]
\[ = ( a^2 + 3a) - (17a + 51)\]
\[ = a(a + 3) - 17(a + 3)\]
\[ = (a - 17)(a + 3)\]