Solving for the Remainder with the Remainder Theorem
Answer:
[tex]3[/tex]
Step-by-step explanation:
According to the Remainder Theorem, if we divide a polynomial, [tex]P(x)[/tex], by [tex]x -\blue a[/tex], the remainder is [tex]P(\blue a)[/tex].
If we let [tex]P(x) = x^2 -1[/tex], the remainder when we divide [tex]P(x)[/tex] by [tex]x -\blue 2[/tex] is [tex]P(\blue 2)[/tex].
The last thing we need to do now is to evaluate [tex]P(\blue 2)[/tex].
[tex]&P(\blue 2) &= &(\blue 2)^2 -1 \\ &P(\blue 2) &= &4 -1 \\ &P(\blue 2) &= &3[/tex]
