Question
when dividing x^3 - 8 bby x - 2, what is the remainder
Answers
GPT-4o mini
To find the remainder when dividing \( x^3 - 8 \) by \( x - 2 \), we can use the Remainder Theorem. According to the theorem, the remainder of the polynomial \( f(x) \) when divided by \( x - c \) is \( f(c) \).
Here, \( f(x) = x^3 - 8 \) and we want to evaluate it at \( c = 2 \):
\[
f(2) = (2)^3 - 8 = 8 - 8 = 0
\]
Thus, the remainder when dividing \( x^3 - 8 \) by \( x - 2 \) is \( \boxed{0} \).
Here, \( f(x) = x^3 - 8 \) and we want to evaluate it at \( c = 2 \):
\[
f(2) = (2)^3 - 8 = 8 - 8 = 0
\]
Thus, the remainder when dividing \( x^3 - 8 \) by \( x - 2 \) is \( \boxed{0} \).