How do you factor the expression $15 x^{2} - 2 x - 8$ $15x^2-2x-8$ ?

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How do you factor the expression $15 x^{2} - 2 x - 8$ $15x^2-2x-8$ ?

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Answer 1 · 2016-01-19T15:28:54

$(5 x - 4) (3 x + 2)$ $(5x-4)(3x+2)$
$15 x^{2} - 12 x + 10 x - 8$ $15x^2-12x+10x-8$

Explanation:

Check for a product what product:
$(- 2 - 3 x) (4 - 5 x)$ $(-2-3x) (4-5x)$
Multiply and test:
$- 8 - 12 x + 10 x + 15 x^{2}$ $-8-12x+10x+15x^2$
Multiply by negative one if you like and have the factors in the answer form
Wich recovers the original quadratic equation

Answer 2 · 2016-01-19T22:00:13

$(5 x - 4) (3 x + 2)$ $(5x-4)(3x+2)$

Explanation:

First, you have to find the zeros of the expression, with the general expression

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+-sqrt(b^2-4ac))/(2a)$

$x = \frac{2 \pm \sqrt{2^{2} - 4 \cdot 15 \cdot 8}}{2 \cdot 15}$ $x=(2+-sqrt(2^2-4*15*8))/(2*15)$

$x = \frac{2 \pm \sqrt{484}}{30}$ $x=(2+-sqrt(484))/(30)$

$x = \frac{2 \pm 22}{30}$ $x=(2+-22)/(30)$

$x = \frac{24}{30}$ $x=24/30$ or $x = - \frac{20}{30}$ $x=-20/30$

$x = \frac{4}{5}$ $x=4/5$ or $x = - \frac{2}{3}$ $x=-2/3$

Finding the zeros we can factorize the expression:

$15 (x - \frac{4}{5}) (x + \frac{2}{3})$ $15(x-4/5)(x+2/3)$

We can continue further to

$5 (x - \frac{4}{5}) \cdot 3 (x + \frac{2}{3})$ $5(x-4/5)*3(x+2/3)$

$(5 x - 4) (3 x + 2)$ $(5x-4)(3x+2)$

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How do you factor the expression $15 x^{2} - 2 x - 8$ $15x^2-2x-8$ ?

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How do you factor the expression $15 x^{2} - 2 x - 8$ $15x^2-2x-8$ ?