How do I use the remainder theorem to divide 2x^2-5x-1 by x-3?

1 Answer
AJ Speller
Oct 9, 2014

The remainder theorem results in the output value of the given polynomial after evaluating it at a specific value of x.

First you solve the divisor by setting it equal to zero.

x-3=0
x=3

This 3 will be used to multiply each coefficient of the of the polynomial.

The coefficients of f(x)=2x^2-5x-1 are 2, -5, and -1.

We begin by multiplying the value of x, which is 3, by the first coefficient.

This product is then added to the next coefficient. The result of the previous operation is then multiplied by 3 and we continue until we reach last coefficient by repeating the steps above.

The numbers in parentheses are are the coefficients.

3*(2)=6

(-5)+6=1

3*(1)=3

(-1)+3=2

By using the remainder theorem we see that f(3)=2

Please see the video below for another example.

Remainder Theorem Example

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