Question

How do you factor `3x^3-x^2-10x+8`?

Answer 1

`(x-1)(3x-4)(x+2)`

Explanation:

`"note the coefficients of the terms"`

`3-1-10+8=0`

`rArrx=1" is a root and " (x-1)" a factor"`

`3x^2(x-1)+2x(x-1)-8(x-1)`

`=(x-1)(3x^2+2x-8)`

`=(x-1)(3x-4)(x+2)`

Answer 2

`(x-1)(x+2)(3x-4)`

Explanation:

`3x^3-x^2-10x+8 = 3x^3-3x^2+2x^2-2x-8x+8` or

`3x^2(x-1)+2x(x-1)-8(x-1) = (x-1)(3x^2+2x-8)` or

`(x-1)(3x^2+6x-4x-8) = (x-1)(3x(x+2)-4(x+2))` or

`(x-1)(x+2)(3x-4)` [Ans]