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Question
Factorize each of the following algebraic expression:
x2 − 22x + 120
Solution
\[\text{ To factorise }x^2 - 22x + 120,\text{ we will find two numbers p and q such that }p + q = - 22\text{ and }pq = 120 . \]
Now,
\[( - 12) + ( - 10) = - 22 \]
and
\[( - 12) \times ( - 10) = 120\]
\[\text{ Splitting the middle term }- 22x \text{ in the given quadratic as }- 12x - 10x,\text{ we get: }\]
\[ x^2 - 22x + 12 = x^2 - 12x - 10x + 120\]
\[ = ( x^2 - 12x) + ( - 10x + 120)\]
\[ = x(x - 12) - 10(x - 12)\]
\[ = (x - 10)(x - 12)\]
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