Question

How do you factor `6x^3+10x^2-32`?

Answer 1

`2 (x-4/3)(3x^2 +8x +12)`

Explanation:

After taking out 2 as a common factor it becomes `2(3x^3 +5x^2 -16)`

In this 3rd degree polynomial, the product of its roots (zeros) would be `-16/3`. Try `x=4/3`, it is found that it is on of the roots. Hence `(x-4/3)` would be a factor. Now carry out long or synthetic division of the polynomial by `(x-4/3)` to have `3x^2 + 8x+12` as a quotient.

The required factorisation would be thus `2 (x-4/3)(3x^2 +8x +12)`