How do you factor #15x^4-50x^3-40x^2#?

1 Answer
Robert C. · Stefan V.
May 25, 2016

#5x^2 ( 3x + 2 ) ( x - 4 )#

Explanation:

Look for the greatest common factors of all the numbers/letters. in this case, #5# is common to #15#, #50#, and #40#, and #x^2# for the #x#'s giving you:

#5x^2 (3x^2 - 10x - 8)#

Since you have a number greater than #1# for the #x^2# inside the brackets, you can factor it further by determining what two number add up to #-10# and multiply to #-24# (derived from #3 xx (-8)#).

#4# and #6# won't work because of the negative numbers, however, #-12# and #2# will.

#5x^2 ( 3x^2 - 12x + 2x - 8)#

Look for the GCFs in the first two variables inside the brackets and then the second two.

#5x^2 [ ( 3x (x - 4) + 2 (x - 4) ]#

Collect like terms and simplify

#5x^2 (3x + 2)(x - 4)#

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