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प्रश्न
Factorize each of the following algebraic expression:
x2 + 12x − 45
योग
उत्तर
\[\text{ To factorise }x^2 + 12x - 45, \text{ we will find two numbers p and q such that } p + q = 12\text{ and pq }= - 45 . \]
Now,
\[15 + ( - 3) = 12 \]
and
\[15 \times ( - 3) = - 45\]
\[\text{ Splitting the middle term 12x in the given quadratic as } - 3x + 15x,\text{ we get: }\]
\[ x^2 + 12x - 45 = x^2 - 3x + 15x - 45\]
\[ = ( x^2 - 3x) + (15x - 45)\]
\[ = x(x - 3) + 15(x - 3)\]
\[ = (x + 15)(x - 3)\]
Now,
\[15 + ( - 3) = 12 \]
and
\[15 \times ( - 3) = - 45\]
\[\text{ Splitting the middle term 12x in the given quadratic as } - 3x + 15x,\text{ we get: }\]
\[ x^2 + 12x - 45 = x^2 - 3x + 15x - 45\]
\[ = ( x^2 - 3x) + (15x - 45)\]
\[ = x(x - 3) + 15(x - 3)\]
\[ = (x + 15)(x - 3)\]
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