Factorize : $x^{2} - 24 x - 180$

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Solution

Given $x^{2} - 24 x - 180$
Here, the middle term $- 24 x = - 30 x + 6 x$ as its product $- 30 x \times (6 x) = - 180 x^{2}$ is same as the product of extreme terms[ $- 180 \times (x^{2}) = - 180 x^{2}$ ]
$= x^{2} - 30 x + 6 x - 180$
$= x (x - 30) + 6 (x - 30)$
$= (x - 30) (x + 6)$
Hence, the factors are $(x - 30) (x + 6)$

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