Question

If \( p(x) = x^4 - 5x + 6 \) and \( q(x) = 2 - x^2 \), then the degree of \( \frac{p(x)}{q(x)} \) is:

• A. \( 2 \)
• B. \( 4 \)
• C. \( 1 \)
• D. \( 3 \)

Hint:

For rational functions: \[ \deg \left( \frac{p(x)}{q(x)} \right) = \deg p(x) - \deg q(x) \]

Answer 1

The Correct Option is B

The degree of a fraction of polynomials is:
\[ \text{Degree of } \frac{p(x)}{q(x)} = \text{Degree of } p(x) - \text{Degree of } q(x) \] Since:
\[ \deg(p(x)) = 4, \quad \deg(q(x)) = 2 \] \[ \deg\left(\frac{p(x)}{q(x)}\right) = 4 - 2 = 2 \]