Question

If f, of, x, equals, 2, x, to the power 5 , minus, 5, x, cubed, minus, 4f(x)=2x
5
−5x
3
−4, then what is the remainder when f, of, xf(x) is divided by x, minus, 1x−1?

Answer 1

To find the remainder when \( f(x) = 2x^5 - 5x^3 - 4 \) is divided by \( x - 1 \), we can use the Remainder Theorem, which states that when a polynomial \( f(x) \) is divided by \( x - c \), the remainder is \( f(c) \).

In this case, we are interested in the remainder when \( f(x) \) is divided by \( x - 1 \). So, we will evaluate \( f(1) \):

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

Calculating this step by step:

\[
= 2(1) - 5(1) - 4
\]
\[
= 2 - 5 - 4
\]
\[
= 2 - 9
\]
\[
= -7
\]

Therefore, the remainder when \( f(x) \) is divided by \( x - 1 \) is

\[
\boxed{-7}
\]