Find the dividend if the divisor is (x+2). quotient is (4x-5) and the remainder is 12.
A. `4x^2+5x+2`
B. `4x^2+3x+2`
C. `4x^2-3x+2`
D. `4x^2+3x-2`

Options

A. B
B. C
C. D
D. A

Answer

To find the dividend given the divisor, quotient, and remainder, we can use the formula:

**Dividend = (Divisor × Quotient) + Remainder**

### Step-by-Step Solution:

1. **Identify the given values:**
- Divisor (D) = \( x + 2 \)
- Quotient (Q) = \( 4x - 5 \)
- Remainder (R) = \( 12 \)

2. **Substitute the values into the formula:**
\[ \text{Dividend} = (x + 2)(4x - 5) + 12 \]

3. **Multiply the divisor and the quotient:**
- Use the distributive property (also known as the FOIL method for binomials):
\[ (x + 2)(4x - 5) = x \cdot 4x + x \cdot (-5) + 2 \cdot 4x + 2 \cdot (-5) \]
- This simplifies to:
\[ 4x^2 - 5x + 8x - 10 \]
- Combine like terms:
\[ 4x^2 + 3x - 10 \]

4. **Add the remainder to the result:**
\[ \text{Dividend} = (4x^2 + 3x - 10) + 12 \]
- Combine the constant terms:
\[ 4x^2 + 3x + 2 \]

5. **Final result:**
- The dividend is:
\[ 4x^2 + 3x + 2 \]

### Conclusion:
The correct answer is **Option B: \( 4x^2 + 3x + 2 \)**.