To solve the problem, we need to analyze the given algebraic expression:
\[ 3x^3 - 6x^2y + 4xy - 2x + y + 6x + x^2y + 9 \]
We will identify the non-constant terms, find their numerical coefficients, and determine the coefficients of \( y \) in the terms that involve \( y \).
### Step 1: Identify Non-Constant Terms
The non-constant terms in the expression are those that contain variables (either \( x \) or \( y \)). The constant term is \( 9 \).
The non-constant terms are:
1. \( 3x^3 \)
2. \( -6x^2y \)
3. \( 4xy \)
4. \( -2x \)
5. \( y \)
6. \( 6x \)
7. \( x^2y \)
### Step 2: Find Numerical Coefficients
Next, we will extract the numerical coefficients from each of the non-constant terms:
1. For \( 3x^3 \), the coefficient is **3**.
2. For \( -6x^2y \), the coefficient is **-6**.
3. For \( 4xy \), the coefficient is **4**.
4. For \( -2x \), the coefficient is **-2**.
5. For \( y \), the coefficient is **1** (since \( y \) can be written as \( 1y \)).
6. For \( 6x \), the coefficient is **6**.
7. For \( x^2y \), the coefficient is **1** (since \( x^2y \) can be written as \( 1x^2y \)).
### Step 3: List the Numerical Coefficients
The numerical coefficients of the non-constant terms are:
- \( 3, -6, 4, -2, 1, 6, 1 \)
### Step 4: Identify Coefficients of \( y \)
Now, we will identify the coefficients of \( y \) in the terms that involve \( y \):
1. From \( -6x^2y \), the coefficient of \( y \) is **-6**.
2. From \( 4xy \), the coefficient of \( y \) is **4**.
3. From \( y \), the coefficient of \( y \) is **1**.
4. From \( x^2y \), the coefficient of \( y \) is **1**.
### Step 5: List the Coefficients of \( y \)
The coefficients of \( y \) in the terms involving \( y \) are:
- \( -6, 4, 1, 1 \)
### Final Answer
- The numerical coefficients of the non-constant terms are: **3, -6, 4, -2, 1, 6, 1**.
- The coefficients of \( y \) in the terms involving \( y \) are: **-6, 4, 1, 1**.
