Factorize : $x^{2} - 8 x + 16$

(x - 4) (x - 5)

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(x - 2) (x - 4)

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(x - 4) (x - 4)

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(x - 4) (x - 3)

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Solution

The correct option is C $(x - 4) (x - 4)$
We have to break up $8 x$ in the given expression into two parts in such a way that their sum is $- 8 x$ the product of their coefficients is $16$
$x^{2} - 8 x + 16$
$= x^{2} - 4 x - 4 x + 16$
$= x (x - 4) - 4 (x - 4)$
$= (x - 4) (x - 4)$

Thus, we can see that $(x - 4)$ and $(x - 4)$ are the two factors of $x^{2} - 8 x + 16$

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