Algebraic Expressions: The Building Blocks of Algebra
An algebraic expression is a collection of numerals, letters, grouping
symbols, and operators (such as +, -, Â·, and
Here are some examples of algebraic expressions:
The algebraic expression 5x2 - 12 - xy3 has three terms:
5x2, -12, and -xy3
A term in an algebraic expression is a quantity joined to other quantities
by the operation of addition or subtraction.
The term -12 is called a constant term because it does not contain a
variable. Note that when a term is subtracted, a negative sign is attached to
the individual term.
The numeric factor of a term is called the coefficient of the variables of
For example, in the algebraic expression 5x2 - 12 - xy3, the coefficient of
x2 is 5 and the coefficient of xy3 is -1.
In the algebraic expression x2, the coefficient
of x2 is 1.
x2 = 1x2
A polynomial is a special kind of algebraic expression.
In a polynomial, each variable must have a whole number exponent.
Here are some examples of polynomials.
|8x + 5
||2x3 - wy2 + 7x - 6
The polynomial 8x + 5
can be written 8x1 + 5x0.
An algebraic expression is not a polynomial if a variable is in the
denominator, inside absolute value bars, or under a radical sign.
For example, these algebraic expressions are not polynomials:
Polynomials with one, two, or three terms have special names.
||Number of terms
x + 7,
x2 - 5x + 7,
6x2 - 5,
-5x3y2 + 6xy - 9
The degree of a term of a polynomial is the sum of the exponents of the
variables in that term. For example,
â€¢ the degree of 8x2y4 is 6 because 2 + 4 = 6;
â€¢ the degree of 43y2 is 2. Note that 4 is not a variable so its
exponent, 3, does not affect the degree of the term.
In the expression 43y2, the exponent 3 does
not contribute to the degree of the term.
That's because 3 is the exponent of a
constant, not a variable.
The degree of a polynomial is equal to the degree of the term with the
For example, the degree of 8x2y4 - 5x3y + 43y2 is 6 because the term with
the highest degree has degree 6.
In 8x2y4 - 5x3y + 43y2, the term with the
highest degree is 8x2y4. It has degree 2 + 4 = 6.
Find the degree of this polynomial: 13w4y3 + 5wy4
- y2 + 32
First, find the degree of each term.
The term with the highest degree is 13w4y3. The degree of this term is 7.
Therefore, the degree of the polynomial is 7.