Polynomials:
Basic Operations and Factoring
Mathematics 17
Institute of Mathematics
Lecture 3
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
1 / 30
Outline
1
Algebraic Expressions and Polynomials
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Division of Polynomials
2
Factoring
Sum and Difference of Two Cubes
Factoring Trinomials
Factoring By Grouping
Completing the Square
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
2 / 30
Algebraic Expressions and Polynomials
An
algebraic expression
is any combination of variables and constants
involving a finite number of basic operations.
3
x
2

5
yz
3
√
2
x
+ 7
y
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
3 / 30
Algebraic Expressions and Polynomials
An
algebraic expression
is any combination of variables and constants
involving a finite number of basic operations.
3
x
2

5
yz
3
√
2
x
+ 7
y
A
polynomial
is an algebraic expression that is a sum of constants
and/or constants multiplied by variables raised to nonnegative integer
exponents.
5
x
3

2
x
4
y
2
+
y
3
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
3 / 30
Algebraic Expressions and Polynomials
An
algebraic expression
is any combination of variables and constants
involving a finite number of basic operations.
3
x
2

5
yz
3
√
2
x
+ 7
y
A
polynomial
is an algebraic expression that is a sum of constants
and/or constants multiplied by variables raised to nonnegative integer
exponents.
5
x
3

2
x
4
y
2
+
y
3
Each addend in a polynomial is called a
term
of the polynomial. The
constant in a term is called its
constant coefficient
.
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
3 / 30
Algebraic Expressions and Polynomials
The sum of the exponents of the variables in a term is called its
degree
.
5
x
2
y
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
4 / 30
Algebraic Expressions and Polynomials
The sum of the exponents of the variables in a term is called its
degree
.
5
x
2
y
:
degree 3
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
4 / 30
Algebraic Expressions and Polynomials
The sum of the exponents of the variables in a term is called its
degree
.
5
x
2
y
:
degree 3
The
degree of a polynomial
is the highest of the degrees of all its
terms.
Example
Degree
5
0
Constant
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
4 / 30
Algebraic Expressions and Polynomials
The sum of the exponents of the variables in a term is called its
degree
.
5
x
2
y
:
degree 3
The
degree of a polynomial
is the highest of the degrees of all its
terms.
Example
Degree
5
0
Constant
2
x

5
1
Linear
Math 17
(Inst. of Mathematics)
Polynomials:
Basic Operations and Factoring
Lec 3
4 / 30
Algebraic Expressions and Polynomials
The sum of the exponents of the variables in a term is called its
degree
.