Question

Let P be the set of polynomials. Let a, b, c, and d be elements of P such that b, c, and d are nonzero elements. Which statement about this quotient must be true?

The quotient is a rational number.
The quotient is an integer.
The quotient is a rational expression.
The quotient is a polynomial.

Answer 1

The quotient is a rational expression that depends on the specific values of the polynomials.

Step-by-step explanation:

The quotient is a rational expression.

In mathematics, a rational expression is a ratio of two polynomials. In this case, the quotient is the result of dividing a polynomial by another polynomial. The quotient may or may not be a rational number or an integer, as it depends on the specific values of the polynomials involved.

For example, if a polynomial of degree 1 is divided by a polynomial of degree 2, the quotient will be a rational expression but not necessarily a rational number. On the other hand, if a polynomial of degree 2 is divided by a polynomial of degree 1, the quotient may be a rational number or an integer.