Question

example 1
determine whether each expression is a polynomial. if it is a polynomial, state the degree of the polynomial.

1. $2x^2 - 3x + 5$
2. $\frac{5mp}{n^2} - \frac{2g}{h}$

Explanation:

Step1: Check expression 1 for polynomial

A polynomial has non-negative integer exponents on variables. For $2x^2 - 3x + 5$, all exponents (2, 1, 0) are non-negative integers. The degree is the highest exponent, so $2$.

Step2: Check expression 2 for polynomial

For $\frac{5np}{n^2} - \frac{2g}{h}$, simplify $\frac{5np}{n^2} = \frac{5p}{n} = 5pn^{-1}$ and $\frac{2g}{h}=2gh^{-1}$. These have negative exponents, which violate polynomial rules.

Answer:

1. $2x^2 - 3x + 5$ is a polynomial, degree = 2
2. $\frac{5np}{n^2} - \frac{2g}{h}$ is not a polynomial