Question

(1 point)
Responses
If f(x) = 3x^5 -4x +1, then what is the remainder when f(x) is divided by x +1
-2
-2

3
3

0
0

2

Answer 1

To find the remainder when \( f(x) = 3x^5 - 4x + 1 \) is divided by \( x + 1 \), we can use the Remainder Theorem. According to the Remainder Theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is \( f(c) \).

In this case, we are dividing by \( x + 1 \), which can be rewritten as \( x - (-1) \). Therefore, we need to evaluate \( f(-1) \):

\[
f(-1) = 3(-1)^5 - 4(-1) + 1
\]
\[
= 3(-1) - 4(-1) + 1
\]
\[
= -3 + 4 + 1
\]
\[
= 2
\]

Thus, the remainder when \( f(x) \) is divided by \( x + 1 \) is \( 2 \). The answer is:

**2**