In the product of (5x+2) and `(2x^(2)-3x+5)`, the sum of the coefficients of `x^(2) and x` is

Options

A. 9
B. -8
C. -9
D. 8

Answer

To solve the problem, we need to find the product of the two expressions \((5x + 2)\) and \((2x^2 - 3x + 5)\), and then determine the sum of the coefficients of \(x^2\) and \(x\) in the resulting polynomial.

### Step-by-Step Solution:

1. **Write down the expressions to be multiplied:**
\[ (5x + 2)(2x^2 - 3x + 5) \]

2. **Distribute each term in the first expression to each term in the second expression:**
- Multiply \(5x\) by each term in \((2x^2 - 3x + 5)\):
- \(5x \cdot 2x^2 = 10x^3\)
- \(5x \cdot (-3x) = -15x^2\)
- \(5x \cdot 5 = 25x\)

- Multiply \(2\) by each term in \((2x^2 - 3x + 5)\):
- \(2 \cdot 2x^2 = 4x^2\)
- \(2 \cdot (-3x) = -6x\)
- \(2 \cdot 5 = 10\)

3. **Combine all the results:**
\[ 10x^3 + (-15x^2 + 4x^2) + (25x - 6x) + 10 \]

4. **Combine like terms:**
- For \(x^2\) terms: \(-15x^2 + 4x^2 = -11x^2\)
- For \(x\) terms: \(25x - 6x = 19x\)

Thus, the polynomial simplifies to:
\[ 10x^3 - 11x^2 + 19x + 10 \]

5. **Identify the coefficients:**
- Coefficient of \(x^2\) is \(-11\)
- Coefficient of \(x\) is \(19\)

6. **Calculate the sum of the coefficients:**
\[ -11 + 19 = 8 \]

### Final Answer:
The sum of the coefficients of \(x^2\) and \(x\) is \(8\).