In the polynomial 6x^3 + 4x^2 + 2x + 3, what is the coefficient of x^2?

Introduction / Context:
This simple algebra question tests understanding of polynomial notation and the meaning of coefficients. We are given a cubic polynomial and asked to identify the coefficient of x^2, which is the number multiplying the x^2 term.

Given Data / Assumptions:

• The polynomial is 6x^3 + 4x^2 + 2x + 3.
• We need the coefficient of the x^2 term.
• All coefficients are real numbers and written in standard form.

Concept / Approach:
A polynomial in x is written as a sum of terms, where each term is a coefficient multiplied by a power of x. The coefficient of x^2 is simply the number that multiplies x^2 in the expression, no further calculation is needed. Identifying it correctly requires only careful reading of the polynomial.

Step-by-Step Solution:
Step 1: Write down the polynomial clearly: 6x^3 + 4x^2 + 2x + 3. Step 2: Identify each term by its power of x. Step 3: The term with x^3 is 6x^3, whose coefficient is 6. Step 4: The term with x^2 is 4x^2, whose coefficient is 4. Step 5: The term with x is 2x, whose coefficient is 2. Step 6: The constant term is 3, which has no x factor. Step 7: Therefore, the requested coefficient of x^2 is 4.

Verification / Alternative check:
We can rewrite the polynomial in standard coefficient list form as a sequence of coefficients for x^3, x^2, x and x^0: 6, 4, 2, 3. The second coefficient in this list corresponds to x^2 and is 4, which matches our identification. No further algebra is required.

Why Other Options Are Wrong:

• Option B: 6 is the coefficient of x^3, not x^2.
• Option C: 3 is the constant term.
• Option D: 2 is the coefficient of x.
• Option E: 0 would mean there is no x^2 term, which is not true because 4x^2 is present.

Common Pitfalls:
Some learners misread the expression or mix up the order of coefficients, especially when polynomials are not written in descending powers. In this question the polynomial is in standard order, so reading carefully is usually enough. Paying attention to the exponent of x ensures the correct coefficient is chosen.

Final Answer:
Thus, the coefficient of x^2 is 4.