Question

Is (x-2) a factor of f(x)=x^3 -8x^2+14x-4?

Answer 1

Yes

Explanation:

Use synthetic division

2 | 1 -8 14 -4

____2 -12_4__

1 -6 2 | 0

Thus,
`(x^3-8x^2+14x-4)/(x-2)=x^2-6x+2\:\text{R}0`, so
`(x-2)` is indeed a factor of f(x) since there's no remainder.