Game Development Reference
In-Depth Information
Polynomials
Polynomials constitute what you can regard as a superset that contains other
types of expressions, such as monomials, binomials, and trinomials. A monomial
consists of a constant coefficient and a single variable. The coefficient must be a
real number. The variable often possesses an exponent. If it does, then the
exponent must be an integer, and it may not be negative. Here are a few examples
of monomials:
5
x
2
,
x
2
,
3
x
4
, 2
2,
0,
Monomials are polynomials, as are binomials and trinomials. A binomial con-
sists of two monomials. A trinomial consists of three monomials. A polynomial,
generally, can consist of a monomial or a combination of monomials. If you
combine monomials to create a polynomial, you use only addition and sub-
traction to do so. To put it differently, a polynomial provides a sum or difference
of monomials, not the quotient or a product. Here are some examples of
polynomials:
1
2
x
, 0
2
x
2
þ
2
x
,
a
3
þ
2
a
,
a
3
,
a
3
,
15
a
, x
þ
Adding or subtracting monomials creates a polynomial. If you multiply or divide
monomials, however, you do not create a polynomial. Also, if the variable in an
expression contains a negative number, then it is not considered a monomial.
Here are a few examples of terms that are not monomials or polynomials:
1
x
þ
2
x
,
2x
þ
3
,
2
þ
x
2
x
In the first expression, 1/
x
represents a negative exponent (
x
1
). The second
expression contains two monomial expressions (2
x
and
x
2
x
2
þ
3), but dividing
one by the other does not create a relation based on addition and subtraction.
With the third example, the situation is the same. Although the expression
includes two monomials, the relation between them is that of division.
Exercise Set 8.1
Determine whether the following expressions constitute polynomials, monomials, or neither
polynomials nor monomials.
a.
1
2
x
2
þ 2x
2
b. 3x
