x^2 + 5x 66 = x^2 + 11x 6x 66 ( ∵ 66 = 11 × 6 ) = #160; x ( x + 11 ) 6 ( x + 11 ) = ( x + 11 ) ( x 6 ) Therefore, x^2 + 5x ...

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Expression Formation

Factorise x2...

Question

Factorize: $x^{2} + 5 x - 66$

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Solution

Given: $x^{2} + 5 x - 66$
Now, using Middle Term Splitting, we have to find two numbers such that their sum is $5 x$ and their product is $- 66 x^{2}$ . Such numbers are $11 x$ and $- 6 x$
$= x^{2} + 11 x - 6 x - 66$
$= x (x + 11) - 6 (x + 11)$
$= (x + 11) (x - 6)$
Therefore,
$x^{2} + 5 x - 66 = (x + 11) (x - 6)$

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