How do you factor #20+6x-2x^2#?

1 Answer
Nov 12, 2015

Answer:

#20+6x-2x^2 = (-2)(x-5)(x+2)#

Explanation:

I (personally) always find it easier to work with expressions in standard form, so I will re-write the given expression as
#color(white)("XXX")-2x^2+6x+20#

As a first step extract the obvious constant factor:
#color(white)("XXX")(-2)(x^2-3x-10)#

To factor the second part, we are looking for factors of #10# whose difference is #3#.
Again with only a bit of consideration we can come up with #(2,5)#

Since the constant term #(-10)# is negative, we know that one of #(2,5)# is negative.
Since the coefficient of #x# (i.e. #(-3)#) is also negative we know that the larger of #(2,5)# should be negative.

Therefore we can factor our expression as
#color(white)("XXX")(-2)(x-5)(x+2)#