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 a quotient in polynomial division is the difference between the degrees of the dividend and divisor. This can help you quickly determine the degree of the resulting quotient.

Answer 1

The Correct Option is B

The degree of a quotient when dividing polynomials is given by:
\[ \text{Degree of Quotient} = \text{Degree of Dividend} - \text{Degree of Divisor}. \] Here, the degree of the dividend \( p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 \) is \( 4 \) and the degree of the divisor \( q(x) = x^2 + 2x - 15 \) is \( 2 \).
Thus, the degree of the quotient is:
\[ 4 - 2 = 2. \] Therefore, the degree of the quotient is \( 2 \).