A monomial is a number, a variable, or a product of numbers and variables that have only positive exponents. A monomial cannot have a variable as an exponent. The tables below show examples of expressions that are and are not monomials.
Determine
whether each expression is a monomial. Explain why or why not.
Alternative Solutions:
– 6ab is a
monomial because it is the product of a number and variables.
2.
m2 – 4
Alternative Solutions:
m2 – 4 is not a monomial because it includes
subtraction.
A monomial or the sum of one or more
monomials is called a polynomial.
For example, x3 + x2
+ 3x + 2 is a polynomial. Each monomial is a term. The terms of the
polynomial are x3, x2, 3x, and 2. Recall that to subtract, you add the opposite.
Special names are given to
polynomials with two or three terms. A polynomial with two terms is a binomial. A
polynomial with three terms is a trinomial. Here are some examples.
Example
State
whether each expression is a polynomial. If it is a polynomial, identify it as
a monomial, binomial, or trinomial.
Alternative Solutions:
The expression 2m – 7 can be
written as 2m + (–7). So, it is a
polynomial. Since it can be written as the sum of two monomials, 2m and –7,
it is a binomial.
4.
x2 + 3x – 4 – 5
Alternative Solutions:
The expression x2 +
3x – 4 – 5 can be written as x2 + 3x + (–9).
So, it is a polynomial. Since it can be written as the sum of three monomials, it
is a trinomial.
Alternative Solutions:
The expression 
is not a polynomial
since 
is not a monomial.
The terms of
a polynomial are usually arranged so that the powers of one variable are in
descending or ascending order.
The degree of a
monomial is the sum of the exponents of the variables.
To find the
degree of a polynomial, find the degree of each term. The greatest of the
degrees of its terms is the degree of the polynomial.
Example
Find the
degree of each polynomial.
6.
5a2 + 3
Alternative Solutions:
The degree of 5a2 +
3 is 2.
Alternative Solutions:
The degree of 6x2 –
4x2y – 3xy is 3.
Polynomials
can be used to represent many real-world situations.
Science
Link
8. The expression 14x3 – 17x2
– 16x + 34 can be used to estimate the number of eggs that a certain
type of female moth can produce. In the expression, x represents the
width of the abdomen in millimeters. About how many eggs would you expect this
type of moth to produce if her abdomen measures 3 millimeters?
Alternative Solutions:
Sumber
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