How do you factor $-12x^2+x+20$ ?

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Answer 1 · 2017-02-28T18:25:28

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

OR

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

OR

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

$-12x^2 +x+20$ is not a comfortable quadratic to work with because of the negative sign at the front.

There are 2 ways around the problem.

$1.$ The last term is positive, so we can just re-arrange the terms to have a positive term at the beginning:

$20+x -12x^2$ which will factorise as $(4-3x)(5+4x)$

$2.$ Sometimes re-arranging will not work because the last term might be negative as well.

Divide $-1$ out as a common factor. This has the effect of changing the signs.

$-12x^2 +x+20 = -1(12x^2 -x-20)$

This factorises as

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

The expression can be left like this, or the negative sign can be multiplied by EITHER of the two brackets. NOT BOTH!

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

OR

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

OR

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

How do you factor -12x^2+x+20-12x^2+x+20?