How do you factor $5 x^{2} - 26 x + 5$ $5x^2 - 26x +5$ ?

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How do you factor $5 x^{2} - 26 x + 5$ $5x^2 - 26x +5$ ?

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Answer 1 · 2017-02-20T19:51:43

$5 x^{2} - 26 x + 5 = (5 x - 1) (x - 5)$ $5x^2-26x+5 = (5x-1)(x-5)$

Explanation:

Given:

$5 x^{2} - 26 x + 5$ $5x^2-26x+5$

Use an AC method:

Find a pair of factors of $A C = 25$ $AC=25$ with sum $B = 26$ $B=26$

The pair $25, 1$ $25, 1$ works.

Use this pair to split the middle term and factor by grouping:

$5 x^{2} - 26 x + 5 = 5 x^{2} - 25 x - x + 5$ $5x^2-26x+5 = 5x^2-25x-x+5$

$5 x^{2} - 26 x + 5 = (5 x^{2} - 25 x) - (x - 5)$ $color(white)(5x^2-26x+5) = (5x^2-25x)-(x-5)$

$5 x^{2} - 26 x + 5 = 5 x (x - 5) - 1 (x - 5)$ $color(white)(5x^2-26x+5) = 5x(x-5)-1(x-5)$

$5 x^{2} - 26 x + 5 = (5 x - 1) (x - 5)$ $color(white)(5x^2-26x+5) = (5x-1)(x-5)$

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How do you factor $5 x^{2} - 26 x + 5$ $5x^2 - 26x +5$ ?

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