How do you factor 10x² - 25x -60?

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How do you factor 10x² - 25x -60?

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Answer 1 · 2015-05-19T01:33:56

You find its roots and then turn them into factors, as follows:

Using Bhaskara:

$\frac{25 \pm \sqrt{625 - 4 (10) (- 60)}}{20}$ $(25+-sqrt(625-4(10)(-60)))/20$
$\frac{25 \pm 55}{20}$ $(25+-55)/20$
$x_{1} = 4$ $x_1=4$ , which is the same as the factor $x - 4 = 0$ $x-4=0$
$x_{2} = - \frac{3}{2}$ $x_2=-3/2$ , which is the same as the factor $2 x + 3$ $2x+3$

Before factoring, let's just remove the common multiplying constant here:

$10 x^{2} - 25 x - 60 = 5 (2 x^{2} - 5 x - 12) = 5 (x - 4) (2 x + 3)$ $10x^2-25x-60=5(2x^2-5x-12)=5(x-4)(2x+3)$

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How do you factor 10x² - 25x -60?

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