How do you factor completely $2x^7 - 32x^3$ ?

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Answer 1 · 2018-03-08T05:33:34

Take out the greatest common factor first.

$=2x^3(x+2)(x-2)(x^2+4)$

First, find the highest number that goes into both terms in the expression (in this case $2x^3$ ).

Divide that out of both terms like so:

$2x^3(x^4-16)$

Then you factor the remaining part as the difference of squares as normal.

$=2x^3(x^2-4)(x^2+4)$

And again:

$=2x^3(x+2)(x-2)(x^2+4)$

How do you factor completely 2x^7 - 32x^32x^7 - 32x^3?