Question

If \( f(x) = x^4 - 2x^3 - x + 2 \) is divided by \( g(x) = x^2 - 3x + 2 \), then the degree of the quotient is:

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

Hint:

For polynomial division, the degree of the quotient is: \[ \text{deg}(f) - \text{deg}(g). \]

Answer 1

The Correct Option is C

The degree of \( f(x) \) is 4 and the degree of \( g(x) \) is 2.
The degree of the quotient is given by:
\[ \text{deg}(f(x)) - \text{deg}(g(x)) = 4 - 2 = 2. \]