Question

What is the remainder of
3x^3 + x^2 − 2x + 7x/x+2?

Answer 1

Interpret the problem as dividing f(x) = 3x^3 + x^2 − 2x + 7 by x + 2. By the Remainder Theorem the remainder is f(−2):

f(−2) = 3(−2)^3 + (−2)^2 − 2(−2) + 7
= 3(−8) + 4 + 4 + 7
= −24 + 15
= −9.

So the remainder is −9. If you meant a different grouping of the terms, tell me and I’ll recompute.