How do you factor $- 6 x^{2} + 31 x - 35$ $-6x^2+31x-35$ ?

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How do you factor $- 6 x^{2} + 31 x - 35$ $-6x^2+31x-35$ ?

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Answer 1 · 2017-03-03T02:56:22

$(3 x - 5) (2 x - 7)$ $(3x-5)(2x-7)$

Explanation:

I started by factoring out a negative one.
$- 6 x^{2} + 31 x - 35$ $-6x^2+31x-35$
$- 1 (6 x^{2} - 31 x + 35)$ $-1(6x^2-31x+35)$

From there, you can split the middle term to accommodate both terms and get the same internal expression. (Some guess and check involved)
$6 x^{2} - 21 x - 10 x + 35$ $6x^2-21x-10x+35$
$3 x (2 x - 7) - 5 (2 x - 7)$ $3x(2x-7)-5(2x-7)$

From there you combine them to get
$(3 x - 5) (2 x - 7)$ $(3x-5)(2x-7)$
and there is your factored form.

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How do you factor $- 6 x^{2} + 31 x - 35$ $-6x^2+31x-35$ ?

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How do you factor $- 6 x^{2} + 31 x - 35$ $-6x^2+31x-35$ ?