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The problem on the screen asks you to factor the polynomial \( 2x^4 + x^3 \) by removing the greatest common monomial factor.

### Step-by-Step Solution:

1. **Identify the greatest common factor (GCF):**
   - The terms in the polynomial are \( 2x^4 \) and \( x^3 \).
   - The common factor in terms of the variables is \( x^3 \) (since \( x^3 \) is the highest power of \( x \) that divides both terms).
   - For the coefficients, the GCF between 2 and 1 is 1.
   - Thus, the GCF of the polynomial is \( x^3 \).

2. **Factor out the GCF:**
   \[
   2x^4 + x^3 = x^3(2x + 1)
   \]

So, the factored form of the polynomial is \( x^3(2x + 1) \).

### Answer:
- The correct choice is **A: \( x^3(2x + 1) \)**.

Would you like more details on this solution or have any further questions?

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Here are five related questions you might find helpful:

1. What is the greatest common factor (GCF) and how is it determined?
2. How do you factor polynomials with more than two terms?
3. What are the steps to factor trinomials completely?
4. How can you check if a polynomial is prime (i.e., cannot be factored)?
5. How do you factor a polynomial when the GCF includes a variable and a coefficient?

**Tip:** Always start by identifying the greatest common factor when factoring polynomials, as this can simplify the problem significantly.

Factor the polynomial by removing the greatest monomial factor: 2x^4 + x^3.

Understand how to factor the polynomial 2x^4 + x^3 by removing the greatest common factor (GCF). This problem involves key algebraic concepts such as factoring and polynomials, and is suitable for students in Grades 8-10.

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