How do you factor #2x^3-3x^2-10x+15#?

1 Answer
George C.
Jul 16, 2017

#2x^3-3x^2-10x+15 = (x^2-5)(2x-3)#

#color(white)(2x^3-3x^2-10x+15) = (x-sqrt(5))(x+sqrt(5))(2x-3)#

Explanation:

Given:

#2x^3-3x^2-10x+15#

Note 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:

#2x^3-3x^2-10x+15 = (2x^3-3x^2)-(10x-15)#

#color(white)(2x^3-3x^2-10x+15) = x^2(2x-3)-5(2x-3)#

#color(white)(2x^3-3x^2-10x+15) = (x^2-5)(2x-3)#

#color(white)(2x^3-3x^2-10x+15) = (x^2-(sqrt(5))^2)(2x-3)#

#color(white)(2x^3-3x^2-10x+15) = (x-sqrt(5))(x+sqrt(5))(2x-3)#

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