How do you factor the expression #x^4+216x#?

1 Answer
Dec 21, 2015

Answer:

Factor out the common factor and then look for a familiar form.
Answer is : #x(x+6)(x^2-6x+36).#

Explanation:

Factoring : #x^4+216x#

Always look for a common factor, here it's an #x.# We get:

#x(x^3+216)#

Lucky for us, 216 is a perfect cube:

#x(x^3+6^3)#

So it's a sum of cubes and we can use the formula:

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

#x(x+6)(x^2-6x+36).#

You can check that the last quadratic doesn't factor.

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