Remainder Theorem

Remainder Theorem (Little Bézout's Theorem)

For a polynomial P(x), P(a) gives the remainder when P(x) is divided by (x − a) .

Note: This theorem is useful for finding the remainder of long division if the quotient is unimportant.

Proof

Since P(x) = (x − a) × Quotient + Remainder

Therefore, P(a) = (a − a) × Quotient + Remainder = Remainder (Shown)

Test Yourself!

Use the applet below to generate questions to check your own understanding of the Remainder Theorem.

Drag the slider to toggle the difficulty from linear to quadratic divisors.

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