How do you factor $4x^3+2x^2-2x-1$ ?

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Answer 1 · 2016-09-01T23:48:58

$4x^3+2x^2-2x-1=(sqrt(2)x-1)(sqrt(2)x+1)(2x+1)$

Notice that the ratio of the first and second terms is the same as that of the third and fourth terms. So this cubic will factor by grouping:

$4x^3+2x^2-2x-1$

$=(4x^3+2x^2)-(2x+1)$

$=2x^2(2x+1)-1(2x+1)$

$=(2x^2-1)(2x+1)$

$=((sqrt(2)x)^2-1^2)(2x+1)$

$=(sqrt(2)x-1)(sqrt(2)x+1)(2x+1)$

How do you factor 4x^3+2x^2-2x-14x^3+2x^2-2x-1?