A3 Polynomials

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.
3x2 − 5yz 3
√
2x + 7y

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.
3x2 − 5yz 3
√
2x + 7y
A polynomial is an algebraic expression that is a sum of constants and/or constants multiplied by variables raised to nonnegative integer exponents. 5x3 − 2x4 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.
3x2 − 5yz 3
√
2x + 7y
A polynomial is an algebraic expression that is a sum of constants and/or constants multiplied by variables raised to nonnegative integer exponents. 5x3 − 2x4 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. 5x2 y

Math 17 (Inst. of Mathematics)

Polynomials: Basic Operations and