Question

How do you factor by grouping `2x^3+12x^2-5x-30`?

Answer 1

`(x+6)(\sqrt2x+\sqrt5)(\sqrt2x-\sqrt5)`

Explanation:

Given polynomial:

`2x^3+12x^2-5x-30`

`=2x^2(x+6)-5(x+6)`

`=(x+6)(2x^2-5)`

`=(x+6)((\sqrt2x)^2-(\sqrt5)^2)`

`=(x+6)(\sqrt2x+\sqrt5)(\sqrt2x-\sqrt5)`