
Simplify the polynomial and write your answer in standard form. Classify your answer by degree and number of terms.

(x+2)(2x2-x-9)

Standard Form (No spaces):  
 

Classification: 

Let's simplify the polynomial \((x + 2)(2x^2 - x - 9)\).

### Step 1: Apply the distributive property (FOIL method)

\[
(x + 2)(2x^2 - x - 9) = x(2x^2 - x - 9) + 2(2x^2 - x - 9)
\]

### Step 2: Distribute \(x\) and \(2\)

\[
= x(2x^2) + x(-x) + x(-9) + 2(2x^2) + 2(-x) + 2(-9)
\]

\[
= 2x^3 - x^2 - 9x + 4x^2 - 2x - 18
\]

### Step 3: Combine like terms

\[
2x^3 + (-x^2 + 4x^2) + (-9x - 2x) - 18
\]

\[
= 2x^3 + 3x^2 - 11x - 18
\]

### Final Answer (in standard form)

\[
2x^3 + 3x^2 - 11x - 18
\]

### Classification:
- **Degree**: 3 (since the highest power of \(x\) is 3)
- **Number of terms**: 4 (since there are 4 terms)

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Do you have any questions or want more details on any of these steps?

Here are 5 related questions to consider:
1. How do you factor polynomials of degree 3?
2. How do you find the roots of a cubic equation?
3. What is the difference between a monomial and a polynomial?
4. How do you determine the degree of a polynomial?
5. What are some common methods to simplify polynomials?

**Tip**: When multiplying polynomials, it's important to distribute each term in the first polynomial to every term in the second one to avoid missing terms.

Simplify the polynomial and write your answer in standard form. Classify your answer by degree and number of terms. (x+2)(2x^2-x-9)

Learn how to simplify the polynomial (x + 2)(2x^2 - x - 9) step-by-step and express it in standard form. This algebra problem explores the distributive property, combining like terms, and classifying the degree and number of terms. Suitable for Grades 8-10.

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