Chapter A.3, Problem 30AYU

To determine

To find: Whether the expression is a polynomial. If it is, give its degree. If it is not, state why not.

Answer to Problem 30AYU

Polynomial; expression is the quotient of two polynomials, the polynomial in the denominator has degree greater than 0, so the expression cannot be a polynomial.

Explanation of Solution

Given:

$\frac{3x^3+2x-1}{x^2+x-1}$

Calculation:

A polynomial in one variable is an algebraic expression of the form $a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0$. If $a_n\ne 0$, it is called the leading coefficient, $a_n{x}^n$ is called the leading term, and $n$ is the degree of the polynomial.

Given, $\frac{3x^3+2x-1}{x^2+x-1}$ is not a polynomial, since the expression is the quotient of two polynomials, the polynomial in the denominator has degree greater than 0, so the expression cannot be a polynomial.