How do you factor $2x^3 + x^2- 6x- 3$ ?

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Answer 1 · 2015-07-21T23:34:17

Factor by grouping to find:

$2x^3+x^2-6x-3$

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

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

Factor by grouping, then use difference of squares identity:

$a^2-b^2 = (a-b)(a+b)$

as follows:

$2x^3+x^2-6x-3$

$=(2x^3+x^2)-(6x+3)$

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

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

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

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

How do you factor 2x^3 + x^2- 6x- 32x^3 + x^2- 6x- 3?