Question

Factorize each of the following algebraic expression:
x² + 14x + 45

Answer 1

\[\text{ To factorise }x^2 + 14x + 45,\text{ we will find two numbers p and q such that }p + q = 14 \text{ and }pq = 45 . \]
Now, 
\[9 + 5 = 14 \]
and 
\[9 \times 5 = 45\]
\[\text{ Splitting the middle term }14x\text{ in the given quadratic as }9x + 5x,\text{ we get: }\]
\[ x^2 + 14x + 45 = x^2 + 9x + 5x + 45\]
\[ = ( x^2 + 9x) + (5x + 45)\]
\[ = x(x + 9) + 5(x + 9)\]
\[ = (x + 5)(x + 9)\]