How do you factor #5w^3-1080#?

1 Answer
George C.
Feb 16, 2017

#5w^3-1080 = 5(w-6)(w^2+6w+36)#

Explanation:

The difference of cubes identity can be written:

#a^3-b^3=(a-b)(a^2+ab+b^2)#

We can use this with #a=w# and #b=6# as follows:

#5w^3-1080 = 5(w^3-216)#

#color(white)(5w^3-1080) = 5(w^3-6^3)#

#color(white)(5w^3-1080) = 5(w-6)(w^2+6w+6^2)#

#color(white)(5w^3-1080) = 5(w-6)(w^2+6w+36)#

The remaining quadratic factor has no linear factors with Real coefficients.

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