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We can solve this problem using **the Remainder Theorem**. The Remainder Theorem states that the remainder when a polynomial \( f(x) \) is divided by \( x - c \) is simply \( f(c) \).

Here, \( f(x) = 5x^4 - 2 \), and we are asked to find the remainder when it is divided by \( x - 1 \). According to the Remainder Theorem, the remainder is \( f(1) \).

Let's calculate \( f(1) \):

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

Thus, the remainder when \( f(x) = 5x^4 - 2 \) is divided by \( x - 1 \) is **3**.

Would you like more details on this process?

Here are some related questions you might find helpful:
1. What is the Remainder Theorem in polynomial division?
2. How do you find the remainder when dividing a polynomial by \( x - c \)?
3. Can the Remainder Theorem be used for any polynomial?
4. What if \( f(x) \) has more complex terms? How would you apply the Remainder Theorem then?
5. How does synthetic division compare to using the Remainder Theorem?

**Tip:** When using the Remainder Theorem, remember that you're always substituting the root \( c \) (from \( x - c \)) into the function \( f(x) \).

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

Learn how to use the Remainder Theorem to find the remainder when the polynomial 5x^4 - 2 is divided by x - 1. This problem involves understanding key concepts from polynomial division and the Remainder Theorem. Suitable for students in Grades 9-11.

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