https://file.aiquickdraw.com/mathbot/file/1726150241442w3ubdd54.jpg

The given expression is:

\[
\frac{x^3 - 2x^2 - 4}{x - 2}
\]

To evaluate this, we need to perform polynomial division (synthetic division or long division). Let's divide \( x^3 - 2x^2 - 4 \) by \( x - 2 \).

### Step 1: Perform synthetic division
The division of the polynomial can be done using synthetic division, but let's first try long division:

1. Divide the leading term of \(x^3\) by the leading term of \(x\), which gives \(x^2\).
2. Multiply \(x^2\) by \(x - 2\), which gives \(x^3 - 2x^2\).
3. Subtract \(x^3 - 2x^2\) from \(x^3 - 2x^2 - 4\), resulting in \(0 - 4 = -4\).

At this point, the remainder is \(-4\), and the quotient is \(x^2\). Therefore:

\[
\frac{x^3 - 2x^2 - 4}{x - 2} = x^2 - \frac{4}{x - 2}
\]

This matches option **d** in the question.

### Answer: 
The correct option is **d**.

Would you like a more detailed explanation or have any further questions? 

Here are some related questions:
1. What is synthetic division and how does it work?
2. Can we solve similar expressions with different divisors?
3. What happens if the remainder is not zero in polynomial division?
4. How do we factor polynomials to simplify expressions?
5. What are some common errors when performing polynomial division?

**Tip**: Synthetic division is usually quicker than long division, especially for linear divisors like \(x - 2\).

Evaluate the expression (x^3 - 2x^2 - 4) / (x - 2)

This problem involves evaluating the rational expression (x^3 - 2x^2 - 4) / (x - 2) using polynomial division. Learn step-by-step how to apply synthetic or long division to simplify the expression. Ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation