Find the sum of the coefficients of `x^(4)` and `x^(2)` in `2(x^(4)+3x^(2)+6x+1)` .

Options

A. 6
B. 7
C. 8
D. 9

Answer

To find the sum of the coefficients of \( x^4 \) and \( x^2 \) in the expression \( 2(x^4 + 3x^2 + 6x + 1) \), we will follow these steps:

### Step 1: Expand the expression
We start by distributing the \( 2 \) across the polynomial inside the parentheses.

\[ 2(x^4 + 3x^2 + 6x + 1) = 2 \cdot x^4 + 2 \cdot 3x^2 + 2 \cdot 6x + 2 \cdot 1 \]

### Step 2: Simplify the expression
Now we simplify the terms:

\[ = 2x^4 + 6x^2 + 12x + 2 \]

### Step 3: Identify the coefficients
Next, we identify the coefficients of \( x^4 \) and \( x^2 \) from the expanded expression:

- The coefficient of \( x^4 \) is \( 2 \).
- The coefficient of \( x^2 \) is \( 6 \).

### Step 4: Calculate the sum of the coefficients
Now, we add the coefficients of \( x^4 \) and \( x^2 \):

\[ \text{Sum} = 2 + 6 = 8 \]

### Conclusion
Thus, the sum of the coefficients of \( x^4 \) and \( x^2 \) is \( 8 \).

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