Question

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

• A. 4
• B. 2
• C. 3
• D. 1

Hint:

The degree of the quotient when dividing polynomials is found by subtracting the degree of the divisor from the degree of the dividend, provided that the division results in a polynomial without remainder.

Answer 1

The Correct Option is B

Step 1: The degree of the quotient when dividing two polynomials is obtained by subtracting the degree of the divisor from the degree of the dividend. Step 2: The degree of \( f(x) \) is 4 (since the highest degree term is \( x^4 \)), and the degree of \( g(x) \) is 2 (since the highest degree term is \( x^2 \)). Thus, the degree of the quotient is: \[ 4 - 2 = 2 \] Thus, the correct answer is (B) 2, reflecting that the degree of the quotient is indeed 2.