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

Question

asked Nov 5, 2022 93.0k views

1 Answer

Simplesthing · Answer 1 · 2022-11-11T13:19:31+0000

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
$P(\blue 2)$ .

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