To simplify the expression \((x - 2)(2x^2 - 3x - 4)\), we need to distribute \(x - 2\) to each term in the second polynomial.

### Step 1: Distribute \(x\) to the terms in \(2x^2 - 3x - 4\):

\[
x \cdot (2x^2) = 2x^3
\]
\[
x \cdot (-3x) = -3x^2
\]
\[
x \cdot (-4) = -4x
\]

### Step 2: Distribute \(-2\) to the terms in \(2x^2 - 3x - 4\):

\[
-2 \cdot (2x^2) = -4x^2
\]
\[
-2 \cdot (-3x) = 6x
\]
\[
-2 \cdot (-4) = 8
\]

### Step 3: Combine all the terms:
\[
2x^3 - 3x^2 - 4x - 4x^2 + 6x + 8
\]

### Step 4: Simplify by combining like terms:
\[
2x^3 - (3x^2 + 4x^2) + (-4x + 6x) + 8 = 2x^3 - 7x^2 + 2x + 8
\]

So, the simplified expression is:
\[
2x^3 - 7x^2 + 2x + 8
\]

Would you like further details on any step?

---

Here are five related questions to expand your understanding:

1. How do you factor cubic expressions like \(2x^3 - 7x^2 + 2x + 8\)?
2. Can the polynomial \(2x^3 - 7x^2 + 2x + 8\) be solved for its roots?
3. How do you perform polynomial division on expressions like this?
4. What is the significance of the degree of a polynomial in its behavior?
5. How would the graph of \(2x^3 - 7x^2 + 2x + 8\) look?

**Tip:** Always double-check your distribution when expanding polynomials—it’s a common place for errors.

Learn how to simplify the polynomial expression (x-2)(2x^2-3x-4) with a detailed step-by-step solution. This problem covers key algebraic concepts such as polynomial multiplication and simplification, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation