Question

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

Answer 1

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