4.3 Classification of expressions and equations

$3x^4$

$\frac{2}{5}{x}^2{y}^6$ .

A fraction occurs, but no variable appears in the denominator.

$5x^3+3x^2-2x+1$

$\frac{3}{x}-16$ .

A variable appears in the denominator.

$4x^2-5x+x^{-3}$ .

A negative exponent appears on a variable.

$5x^3$ is a monomial of degree 3.

$60a^5$ is a monomial of degree 5.

$21b^2$ is a monomial of degree 2.

8 is a monomial of degree 0. We say that a nonzero number is a term of 0 degree since it could be written as $8x^0$ . Since $x^0=1(x\ne 0)$ , $8x^0=8$ . The exponent on the variable is 0 so it must be of degree 0. (By convention, the number 0 has no degree.)

$4x$ is a monomial of the first degree. $4x$ could be written as $4x^1$ . The exponent on the variable is 1 so it must be of the first degree.

$4x^2{y}^5$ is a monomial of degree $2+5=7$ . This is a 7th degree monomial.

$37a{b}^2{c}^6{d}^3$ is a monomial of degree $1+2+6+3=12$ . This is a 12th degree monomial.

$5xy$ is a monomial of degree $1+1=2$ . This is a 2nd degree monomial.

$2x^3+6x-1$ is a trinomial of degree 3. The first term, $2x^3$ , is the term of the highest degree. Therefore, its degree is the degree of the polynomial.

$7y-10y^4$ is a binomial of degree 4.

$a-4+5a^2$ is a trinomial of degree 2.

$2x^6+9x^4-x^7-8x^3+x-9$ is a polynomial of degree 7.