Adding And Subtracting Polynomials
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2NAME
DATE
PERIOD
8-1
Study Guide and Intervention
Adding and Subtracting Polynomials
Polynomials in Standard Form
A polynomial is a monomial or a sum of
monomials. A binomial is the sum of two monomials, and a trinomial is the sum of three
monomials. Polynomials with more than three terms have no special name. The degree of a
monomial is the sum of the exponents of all its variables. The degree of the polynomial is
the same as the degree of the monomial term with the highest degree.
The terms of a polynomial are usually arranged so that the terms are in order from greatest
degree to least degree. This is called the standard form of a polynomial.
Example
Determine whether each expression is a polynomial. If so, identify
the polynomial as a monomial, binomial, or trinomial. Then find the degree of the
polynomial.
Monomial, Binomial,
Degree of the
Expression
Polynomial?
or Trinomial?
Polynomial
Yes. 3x - 7xyz = 3x + (-7xyz),
3x - 7xyz
binomial
3
which is the sum of two monomials
-25
Yes. -25 is a real number.
monomial
0
3
-4
=
−
No. 3 n
, which is not a
+ 3n
-4
3
none of these
—
7n
4
n
monomial
Yes. The expression simplifi es to
+ 4x + x + 4 + 2x
+ 7x + 4, which is the sum of
9x
3
9x
3
trinomial
3
three monomials
Exercises
Determine whether each expression is a polynomial. If it is a polynomial, find the
degree and determine whether it is a monomial, binomial, or trinomial.
3
yes; 0; monomial
no
−
+ 5
1. 36
2.
q
2
yes; 1; binomial
yes; 3; trinomial
3. 7x - x + 5
h - 7gh + 2
4. 8g
2
1
no
yes; 2; binomial
−
+ 5y - 8
6. 6x + x
5.
2
4 y
2
Write each polynomial in standard form. Identify the leading coefficient.
7. x
+ x
- x
8. x
+ 4x
- 7x
+ 1
9. -3x
- x
+ 2x
3
5
2
4
3
5
6
5
8
+ x
- x
; 1
-7x
+ x
+ 4x
+ 1; -7
2x
- 3x
- x
; 2
5
3
2
5
4
3
8
6
5
x
- x
11. 3x + 5x
- 2 - x
12. -2x
+ x - 4x
+ 3
10. 2x
7
8
4
2
4
5
-x
+ 2x
; -1
5x
- x
+ 3x - 2; 5
-4x
- 2x
+ x + 3; -4
8
7
4
2
5
4
5
Chapter 8
Glencoe Algebra 1
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