Remainder Theorem
Remainder Theorem (Little Bézout's 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) .
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
Proof
Since P(x) = (x − a) × Quotient + Remainder
Since P(x) = (x − a) × Quotient + Remainder
Therefore, P(a) = (a − a) × Quotient + Remainder = Remainder (Shown)
Therefore, P(a) = (a − a) × Quotient + Remainder = Remainder (Shown)
Test Yourself!
Test Yourself!
Use the applet below to generate questions to check your own understanding of the Remainder Theorem.
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.
Drag the slider to toggle the difficulty from linear to quadratic divisors.