Question

If \( p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 \) is divided by \( q(x) = x^2 + 2x - 15 \), then the degree of the quotient is:

• A. 4
• B. 2
• C. 3
• D. 1

Hint:

The degree of the quotient is the difference between the degrees of the dividend and divisor.

Answer 1

The Correct Option is C

When dividing a polynomial by another polynomial, the degree of the quotient is the difference between the degrees of the numerator and the denominator. The degree of \( p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 \) is 4, and the degree of \( q(x) = x^2 + 2x - 15 \) is 2. Thus, the degree of the quotient is: \[ 4 - 2 = 2. \] Thus, the correct answer is \( \boxed{2} \).