How do you factor $5 x^{2} + 29 x - 6$ $5x^2 +29x - 6$ ?

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How do you factor $5 x^{2} + 29 x - 6$ $5x^2 +29x - 6$ ?

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Answer 1 · 2016-05-14T21:33:15

$5 x^{2} + 29 x - 6 = (5 x - 1) (x + 6)$ $5x^2+29x-6=(5x-1)(x+6)$

Explanation:

Use an AC method:

Find a pair of factors of $A C = 5 \cdot 6 = 30$ $AC=5*6=30$ with difference $B = 29$ $B=29$ .

The pair $30, 1$ $30, 1$ works.

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

$5 x^{2} + 29 x - 6$ $5x^2+29x-6$

$= 5 x^{2} + 30 x - x - 6$ $=5x^2+30x-x-6$

$= (5 x^{2} + 30 x) - (x + 6)$ $=(5x^2+30x)-(x+6)$

$= 5 x (x + 6) - 1 (x + 6)$ $=5x(x+6)-1(x+6)$

$= (5 x - 1) (x + 6)$ $=(5x-1)(x+6)$

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How do you factor $5 x^{2} + 29 x - 6$ $5x^2 +29x - 6$ ?

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