If the polynomial `a-2x+5x^(2)` is divided by `x-2` , it leaves remainder `7` . Then, the value of a is

Options

A. `-9`
B. `9`
C. `7`
D. `-7`

Answer

To solve the problem, we need to find the value of \( a \) in the polynomial \( P(x) = a - 2x + 5x^2 \) given that when this polynomial is divided by \( x - 2 \), it leaves a remainder of \( 7 \).

### Step-by-step Solution:

1. **Understand the Remainder Theorem**: According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder is \( P(c) \). In this case, we will evaluate \( P(2) \) since we are dividing by \( x - 2 \).

2. **Substitute \( x = 2 \) into the polynomial**:
\[ P(2) = a - 2(2) + 5(2^2) \]

3. **Calculate \( P(2) \)**:
\[ P(2) = a - 4 + 5(4) \]
\[ P(2) = a - 4 + 20 \]
\[ P(2) = a + 16 \]

4. **Set the expression equal to the remainder**: We know from the problem that \( P(2) = 7 \).
\[ a + 16 = 7 \]

5. **Solve for \( a \)**:
\[ a = 7 - 16 \]
\[ a = -9 \]

### Final Answer:
The value of \( a \) is \( -9 \).

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