algebra 2 question

Question

I'm trying to find the remainder please help I'm stumped

f(x)=3x^6+82^3+27

Answer 1

y = 3x^6 +18x -27

factor it and let z=x^3

= 3(z^2+ 6z +9)

= 3(z +3)(z+3)

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

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

if you divide the original 6 degree polynomial by any of its factors the quotient is the product of the other factors and the remainder = 0

but I just made the problem more factor-able.

as given It reads

3x^6+82x^3 +27

divide that by x+1, by long or synthetic division and you get a remainder

-1 3 0 0 82 0 0 27

quotient = 3 -3 3 79 -79 79 -46 where -46 is the Remainder of -46/(x+1) is the Remainder

so x+1 is not a factor of the 6 degree polynomial