Question

How do you factor the expression `6x^3 + 4x^2 + 3x + 2`?

Answer 1

Factor by grouping to find:

`6x^3+4x^2+3x+2`

`=(2x^2+1)(3x+2)`

`=(sqrt(2)x-i)(sqrt(2)x+i)(3x+2)`

Explanation:

Factor by grouping:

`6x^3+4x^2+3x+2`

`=(6x^3+4x^2)+(3x+2)`

`=2x^2(3x+2) + 1(3x+2)`

`=(2x^2+1)(3x+2)`

The remaining quadratic factor has no linear factors with Real coefficients, but can be factored as a difference of squares using Complex coefficients:

`=((sqrt(2)x)^2-i^2)(3x+2)`

`=(sqrt(2)x-i)(sqrt(2)x+i)(3x+2)`