Question

Factorize each of the following algebraic expression:
x² − 4x − 21

Answer 1

\[\text{ To factorise }x^2 - 4x - 21,\text{ we will find two numbers p and q such that }p + q = - 4\text{ and }pq = - 21 . \]
Now, 
\[3 + ( - 7) = - 4 \]
and 
\[3 \times ( - 7) = - 21\]
\[\text{ Splitting the middle term }- 4x\text{ in the given quadratic as }- 7x + 3x, \text{ we get: }\]
\[ x^2 - 4x - 21 = x^2 - 7x + 3x - 21\]
\[ = ( x^2 - 7x) + (3x - 21)\]
\[ = x(x - 7) + 3(x - 7)\]
\[ = (x + 3)(x - 7)\]