If `(14x^(2)+13x-15)` is divided by `(7x-4)`, the degree of the remainder is

Options

A. 1
B. 2
C. 0
D. 3

Answer

To determine the degree of the remainder when dividing \( 14x^2 + 13x - 15 \) by \( 7x - 4 \), we can follow these steps:

### Step 1: Understand the Division of Polynomials
When dividing a polynomial \( P(x) \) by a polynomial \( D(x) \), the result can be expressed as:
\[ P(x) = D(x) \cdot Q(x) + R(x) \]
where \( Q(x) \) is the quotient and \( R(x) \) is the remainder.

### Step 2: Identify the Degrees of the Polynomials
- The degree of the polynomial \( P(x) = 14x^2 + 13x - 15 \) is 2 (the highest power of \( x \)).
- The degree of the polynomial \( D(x) = 7x - 4 \) is 1.

### Step 3: Determine the Degree of the Remainder
According to polynomial division, the degree of the remainder \( R(x) \) must be less than the degree of the divisor \( D(x) \). Since the degree of \( D(x) \) is 1, the degree of the remainder \( R(x) \) must be less than 1.

### Step 4: Conclude the Degree of the Remainder
The only polynomial with a degree less than 1 is a constant polynomial (degree 0). Therefore, the degree of the remainder when dividing \( 14x^2 + 13x - 15 \) by \( 7x - 4 \) is 0.

### Final Answer:
The degree of the remainder is **0**.

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