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
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