Question

Divide 3x2 + 6 by 3x – 3.

Which expression represents the quotient and remainder?

x +
x + 1 +
x + 1 +
x

Answer 1

Divide using polynomial long division:

(3x^2 + 0x + 6) ÷ (3x − 3):

1) 3x^2 ÷ 3x = x. Multiply: x(3x−3)=3x^2−3x. Subtract → 3x+6.
2) 3x ÷ 3x = 1. Multiply: 1(3x−3)=3x−3. Subtract → remainder 9.

So the quotient is x + 1 and the remainder is 9. The division gives

3x^2+6
------- = x + 1 + 9/(3x−3) = x + 1 + 3/(x−1).
3x−3