If $x^{2} - 8 x + 13$ can be written as (x – a)(x – 6) + 1. Find the value of a.

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Solution

$x^{2} - 8 x + 13 = (x - a) (x - 6) + 1$
or, $x - a = \frac{x^{2} - 8 x + 12}{x - 6}$

$\begin{matrix} x - 2 x - 6 x^{2} - 8 x + 12 x^{2} - 6 x - ------ - - 2 x + 12 - 2 x + 12 - -------- - 0 \end{matrix}$

Hence, a = 2

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