Consider each given algebraic statement.

Question

i). Classify each as an equation or an expression.

ii). For each expression classify it as polynomial, monomial, binomial, trinomial, and/or none of these.

iii). Also, for each polynomial: list each term, the degree of each term, and the coefficient of each term.

(If it is not an expression, you skip ii part, and if it is not a polynomial expression, you skip iii part).

a). 4x⁸-y³+33/14z (33/14 is a fraction, I just cannot write it like that because I do not have a special keyboard/program for it).

b). 4c

99u+v

c). 6a+5b=110

d). -512mnp

Answer 1

Hello, Yuliya,

The way to handle a fraction is to place parentheses around it: 4x⁸-y³+33/14z may be written 4x⁸-y³+(33/14)z

Expressions are a number, a variable, or a combination of numbers and variables and operation symbols. An equation consists of two expressions connected by an equal sign.

I'll note the "term, the degree of each term, and the coefficient of each term" by identifying them as written in the equation, "the term" with the leading number as the coefficient, the degree as the exponent.

a). 4x⁸-y³+(33/14)z is an expression since there is no "=" sign. Polynomial. 4x⁸, -1y³ , (33/14)z¹

b). 4c/(99u+v) Expression, monomial 4c¹ , 99u¹ 1v¹

c). 6a+5b=110 Equation. monomial, 6a¹, 5b¹

d). -512mnp Expression, monomial, -512m¹ , 1n¹ , 1p¹

Bob