Remainder of (x^2 – 5x + 6) / (x – 2)?

Explanation

• By the remainder theorem, dividing by (x − 2) leaves a remainder equal to P(2).
• Work it out: P(2) = 2² − 5(2) + 6 = 4 − 10 + 6 = 0.
• A remainder of 0 means (x − 2) divides the expression exactly, so it is a factor.
• Factorising confirms it: x² − 5x + 6 = (x − 2)(x − 3).
• Change the divisor to (x − 1) and the remainder becomes P(1) = 1 − 5 + 6 = 2, so the divisor decides the value.