Find the remainder when x3 – 2x2 + 5x – 4 is divided by (x – 5).

We can find the remainder when \( x^3 - 2x^2 + 5x - 4 \) is divided by \( x - 5 \) using **synthetic division** or the **Remainder Theorem**.

### Using the Remainder Theorem:
The Remainder Theorem states that when a polynomial \( f(x) \) is divided by \( x - c \), the remainder is \( f(c) \). In this case, we are dividing by \( x - 5 \), so we need to evaluate \( f(5) \).

The given polynomial is:
\[
f(x) = x^3 - 2x^2 + 5x - 4
\]

Now substitute \( x = 5 \):
\[
f(5) = 5^3 - 2(5^2) + 5(5) - 4
\]
\[
f(5) = 125 - 2(25) + 25 - 4
\]
\[
f(5) = 125 - 50 + 25 - 4
\]
\[
f(5) = 96
\]

Thus, the remainder when \( x^3 - 2x^2 + 5x - 4 \) is divided by \( x - 5 \) is **96**.

### Do you want more details or have any questions?

Here are 5 related questions you might be interested in:
1. How do you perform synthetic division to find the quotient and remainder?
2. What is the relationship between the Remainder Theorem and the Factor Theorem?
3. How does polynomial long division work compared to synthetic division?
4. What happens when you divide a polynomial by a higher-degree polynomial?
5. Can the Remainder Theorem be used for polynomials with complex coefficients?

**Tip**: The Remainder Theorem is a quick way to check for divisibility—if the remainder is zero, the divisor is a factor!

Find the remainder when x^3 – 2x^2 + 5x – 4 is divided by (x – 5).

Discover how to find the remainder when the polynomial x^3 – 2x^2 + 5x – 4 is divided by x – 5 using the Remainder Theorem. This problem introduces key algebraic concepts, including polynomial division and remainder evaluation. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation