Question

Divide. Fill in the quotient and the remainder.
(x2–3x+3)÷(x–2)=
+
x–2

Answer 1

(x^2 − 3x + 3) ÷ (x − 2):

Using synthetic division (2): coefficients 1, −3, 3 → bring down 1; 1·2=2 → −3+2=−1; −1·2=−2 → 3+(−2)=1.

Quotient: x − 1, remainder: 1.

So (x^2 − 3x + 3)/(x − 2) = x − 1 + 1/(x − 2).