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)

Related questions
See all questions in Factoring Completely
Impact of this question
3262 views around the world
You can reuse this answer
Creative Commons License