Factories: x^2+12 x-45 - Vidyadip

Question

Factories:
$x^2+12 x-45$

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Answer

To factories $x^2+12 x-45$, we will find two number $p$ and $q$ such that $p+q=12$ and $p q=-45$ Now, $15+(-3)=12$ and $15 \times(-3)=-45$
Splitting the middle term $12 x$ in the given quadratic as $-3 x+15 x$, we get:
$x^2+12 x-45$
$=x^2-3 x+15 x-45$
$=\left(x^2-3 x\right)+(15 x-45)$
$=x(x-3)+15(x-3)$
$=(x-3)(x+15)$

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