How do you factor 15x^2 + 4x - 4 = 0?

May 8, 2016

$\left(3 x + 2\right) \left(5 x - 2\right)$

Explanation:

It is a matter of spotting possible combinations and trying them out. They can be tried out on paper or in your head.

Factors of 15 $\to${1,15} ; {3,5}

Factors of 4 $\to${1,4} ; {2,2}

Cross link factors of 4 with factors of 15

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$\left(1 \times 15\right) - \left(4 \times 1\right) = 11 \text{ So this is no good for obtaining } 4 x$
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$\left(2 \times 15\right) - \left(2 \times 1\right) = 28 \text{ So this is no good for obtaining } 4 x$
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$\left(3 \times 4\right) - \left(1 \times 5\right) = 7 \text{ So this is no good for obtaining } 4 x$
$\left(\textcolor{g r e e n}{2 \times 5}\right) - \left(\textcolor{red}{2 \times 3}\right) = 4 \textcolor{b r o w n}{\text{ this is the combination we need}}$
$\left(\textcolor{red}{3} x \textcolor{g r e e n}{+ 2}\right) \left(\textcolor{g r e e n}{5} x \textcolor{red}{- 2}\right)$