Question

What is the remainder when a polynomial (x^2-1) is divided by (x-2)​

Answer 1

Solving for the Remainder with the Remainder Theorem

Answer:

`3`

Explanation:

According to the Remainder Theorem, if we divide a polynomial,
`P(x)`, by
`x -\blue a`, the remainder is
`P(\blue a)`.

If we let
`P(x) = x^2 -1`, the remainder when we divide
`P(x)` by
`x -\blue 2` is
`P(\blue 2)`.

The last thing we need to do now is to evaluate
`P(\blue 2)`.

`&P(\blue 2) &= &(\blue 2)^2 -1 \\ &P(\blue 2) &= &4 -1 \\ &P(\blue 2) &= &3`