How do you factor $-25x^2-70x+120$ ?

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Answer 1 · 2015-05-30T10:03:33

First separate out the common factor $-5$ ...

$-25x^2-70x+120 = -5(5x^2+14x-24)$

Then, using a version of the AC Method, look for a pair of factors of $5*24 = 120$ , whose difference is $14$ ...

$20 xx 6 = 120$
$20 - 6 = 14$

Then use the pair we found to split the middle term and factor by grouping...

$-5(5x^2+14x-24)$

$=-5(5x^2+20x-6x-24)$

$=-5((5x^2+20x)-(6x+24))$

$=-5(5x(x+4)-6(x+4))$

$=-5(5x-6)(x+4)$

How do you factor -25x^2-70x+120-25x^2-70x+120?