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:

The degree of a rational function \( \frac{p(x)}{q(x)} \) is found by subtracting the degree of the denominator from the degree of the numerator.

Answer 1

The Correct Option is A

Step 1: Identify the degrees of \( p(x) \) and \( q(x) \) - The highest degree term in \( p(x) \) is \( x^4 \), so \( \deg(p(x)) = 4 \). - The highest degree term in \( q(x) \) is \( -x^2 \), so \( \deg(q(x)) = 2 \). 

Step 2: Compute the degree of \( \frac{p(x)}{q(x)} \) \[ \deg \left( \frac{p(x)}{q(x)} \right) = \deg(p(x)) - \deg(q(x)) \] \[ = 4 - 2 = 2 \] Thus, the correct answer is \( 2 \).