How do you factor $x^4 + 8x^3 - 2x^2 - 16x$ ?

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Answer 1 · 2016-04-09T23:35:35

$x^4+8x^3-2x^2-16x=x(x-sqrt(2))(x+sqrt(2))(x+8)$

First note that all of the terms are divisible by $x$ , so separate that out as a factor first, then factor by grouping...

$x^4+8x^3-2x^2-16x$

$=x(x^3+8x^2-2x-16)$

$=x((x^3+8x^2)-(2x+16))$

$=x(x^2(x+8)-2(x+8))$

$=x(x^2-2)(x+8)$

$=x(x-sqrt(2))(x+sqrt(2))(x+8)$

How do you factor x^4 + 8x^3 - 2x^2 - 16xx^4 + 8x^3 - 2x^2 - 16x?