Advanced Functions (MHF4U) · Polynomial and Rational Functions

Remainder theorem

Use the remainder theorem to find the remainder when a polynomial is divided by (x - k), without doing long division. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MHF4U-PR1.1

Try one

Use the remainder theorem to find the remainder when P(x) is divided by (x - 2).

P(x) = 3x2 - 3x + 4

Answer: 10

See one solved, step by step

Use the remainder theorem to find the remainder when P(x) is divided by (x + 2).

P(x) = 5x3 + x2 + x + 4
📘 Worked solution
1By the remainder theorem, dividing by (x + 2) leaves a remainder of P(−2).The remainder theorem lets you skip the division entirely.
2P(−2) = 5(−2)3 + 1(−2)2 + 1(−2)1 + 4Substitute x = -2 into P(x).
3= −34Simplify the powers and add the terms.

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