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Question
Factorize each of the following algebraic expression:
x2 − 11x − 42
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Solution
\[\text{ To factorise }x^2 - 11x - 42,\text{ we will find two numbers p and q such that }p + q = - 11\text{ and }pq = - 42 . \]
Now,
\[3 + ( - 14) = - 22 \]
and
\[3 \times ( - 14) = 42\]
\[\text{ Splitting the middle term }- 11x\text{ in the given quadratic as }- 14x + 3x, \text{ we get: }\]
\[ x^2 - 11x - 42 = x^2 - 14x + 3x - 42\]
\[ = ( x^2 - 14x) + (3x - 42)\]
\[ = x(x - 14) + 3(x - 14)\]
\[ = (x + 3)(x - 14)\]
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