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)#