Adding and Subtracting Polynomials 85
d. 3 x^5
Step 1. Check whether 3 x^5 meets the criteria for a monomial.
3 x^5 is a term that is a product of one variable raised to a positive
integer power, with an explicit coeffi cient of 3, so it is a monomial.
e. 27
Step 1. Check whether 27 meets the criteria for a monomial.
27 is a constant, so it is a monomial.
f. 4 xy−^323
Step 1. Check whether 4 xy−^32 meets the criteria for a monomial.
4 xy−^32 contains a negative exponent, so it is not a monomial.
g. 6 x
Step 1. Check whether 6 x meets the criteria for a monomial.
6
1
xx 6 2 contains a fractional exponent, so it is not a monomial.
Polynomials
A polynomial is a single monomial or a sum of monomials. A polyno-
mial that has exactly one term is a monomial. A polynomial that has
exactly two terms is a binomial. A polynomial that has exactly three
terms is a trinomial. A polynomial that has more than three terms is
just a general polynomial.
Problem State the most specifi c name for the given polynomial.
a. x^2 − 1
b. 8 ab^3336644
c. xx^2 + 414 xx 2
d.
1
3
xz^232
e. − 2 xxxx^54 +++ 555 4 − 37332 − 77 ++x 4
