Question

If \( p(y) = (y + 1)(y^3 + 2)(y^4 + 6) \) and \( g(y) = y^2 - 3y + 1 \), then the degree of \( \frac{p(y)}{g(y)} \) is:

• A. 6
• B. 3
• C. 5
• D. 4

Hint:

The degree of the quotient of two polynomials is the degree of the numerator minus the degree of the denominator.

Answer 1

The Correct Option is A

The degree of a polynomial is the highest power of the variable in the polynomial.
The degree of the product of two polynomials is the sum of the degrees of the polynomials involved.
The degree of \( p(y) = (y + 1)(y^3 + 2)(y^4 + 6) \) is: \[ \text{Degree of } (y + 1) = 1, \quad \text{Degree of } (y^3 + 2) = 3, \quad \text{Degree of } (y^4 + 6) = 4 \] \[ \text{Degree of } p(y) = 1 + 3 + 4 = 8 \]
The degree of \( g(y) = y^2 - 3y + 1 \) is: \[ \text{Degree of } g(y) = 2 \]
The degree of the quotient \( \frac{p(y)}{g(y)} \) is: \[ \text{Degree of} \left( \frac{p(y)}{g(y)} \right) = 8 - 2 = 6 \]