Question

3 | (x^3-6x^2+11x-6)

Answer 1

Surely you aren't asking for help doing synthetic division, are you?

Answer 2

prove the above
3 divides that polynomial

(i know the answer already )

Answer 3

(or disprove)

Answer 4

\( (x^3-6x^2+11x-6) \equiv ( x^3+ 11x) \equiv (x^3-x) \mod 3\)

Answer 5

\( (x)(x^2-1) \equiv x(x+1)(x-1) \equiv 0 \mod 3\)

assuming x is an integer, product of 3 consecutive integers are divisible by 3

Answer 6

and it factors to \((x-1)(x-2)(x-3)\)...