The Mathematics 11
Competency Test
Terminology of Algebraic
Expressions
In this note we give brief descriptions and illustrations of some names of things encountered in
algebra.
An algebraic expression is a sequence of numbers and literal symbols together with arithmetic
operation symbols and perhaps pairs of brackets. When the literal symbols are replaced by
actual numbers, it should be possible to reduce the resulting numerical expression to a single
numerical value.
Examples of algebraic expressions are:

3 x  5y  7

6  x  5   24 x

5 x2

6x3  5x 2  8x  7

2
3x
2
 7 x  1
4
Algebraic expressions consist of one or more terms. The terms of the expression are the parts of
the expression which are separated by ‘+’ or ‘-‘ signs.
Thus, the expression:

3 x  5y  7
has 3 terms

6  x  5   24 x
has 2 terms

5 x2
has 1 term

6x  5x  8x  7

2
3
3x
2
2
 7 x  1
has 4 terms
4
has 1 term
Terms can be products of two or more factors. A product results when two or more quantities
are multiplied together. The quantities being multiplied together to form a product are called its
factors. Thus
 ‘3x’ is the product of two factors, ‘3’ and ‘x’; or ‘3’ and ‘x’ are the factors of the
product ‘3x’
 ‘6x2y’ is the product of three factors: ‘6’, ‘x2’, and ‘y’
Of course, ‘x2’ could itself be regarded as the product of two factors: ‘x’ and ’x’. In that case, 6x2y
becomes the product of four factors.
Often a term is a product of a constant or number and a part which is a literal symbol or a product
or two or more literal symbols. The numerical factor is often referred to as the coefficient or
numerical coefficient of the term. Thus
David W. Sabo (2003)
Terminology of Algebraic Expressions
Page 1 of 2
 the term ‘3x’ has the numerical coefficient ‘3’
 the term ‘6x2y’ has the numerical coefficient ‘6’,
etc.
The word coefficient is also used more generally to refer to a factor or group of factors in a term.
Thus, for example, in the term 6x2y,
‘6x2’ is the coefficient of ‘y’
and
‘y’ is the coefficient of ‘6x2’
Terms which have identical symbolic parts are said to be like terms. Logically, two terms with
different symbolic parts would be called unlike terms. So
 3x2y and 7x2y are like terms (the symbolic part in both cases is ‘x2y’)
but
 3x2y and 7xy2 are unlike terms, because the symbolic part of the first one is x 2y,
which is different from xy2, the symbolic part of the second one.
There are specific names for expressions which indicate how many terms they contain:
monomials are expressions with just one term
for example: 5, 6x2y, 3x, 7xyz, etc. are monomials
binomials are expressions with two terms:
for example: x + y, 3x2 – 4y, 5 + 2x, etc., are binomials
trinomials are expressions with 3 terms
for example
5 x 2  2xy  3y 2
is a trinomial
7 x  5 y  3z
is a trinomial
multinomials are expressions with several terms
polynomials are expressions with two or more terms in which the symbolic part of each
term is a power of a single symbol (the same one in all terms). The degree of a
polynomial is the highest power that it contains.
for example:
3 x 2  2 x  5 is a polynomial of degree 2 (or, a polynomial of the second
degree)
5 x 7  3 x 4  9 x 3  7 x 2  2 is a polynomial of degree 7.
David W. Sabo (2003)
Terminology of Algebraic Expressions
Page 2 of 2