Question

If \( p(y) = (y+1)(y^3+2)(y^4+6) \) and \( g(y) = y^2 - 3y +1 \), then the degree of \( \frac{p(y)}{g(y)} \) is:

• A. \( 6 \)
• B. \( 3 \)
• C. \( 5 \)
• D. \( 4 \)

Hint:

The degree of a product of polynomials is the sum of their degrees. The degree of a rational function \( \frac{p(x)}{g(x)} \) is: \[ \text{Degree} = \text{Degree of numerator} - \text{Degree of denominator}. \]

Answer 1

The Correct Option is A

The degree of a polynomial is the highest power of \( y \).
- Degree of \( p(y) \):
\[ (y+1) \Rightarrow \text{Degree } 1. \] \[ (y^3+2) \Rightarrow \text{Degree } 3. \] \[ (y^4+6) \Rightarrow \text{Degree } 4. \] \[ \text{Total Degree of } p(y) = 1 + 3 + 4 = \] - Degree of \( g(y) \):
\[ y^2 - 3y + 1 \Rightarrow \text{Degree } 2. \] Thus, the degree of \( \frac{p(y)}{g(y)} \) is:
\[ 8 - 2 = 6. \]