Lecture 3 - Polynomials Basic Operations and Factoring Mathematics 17 Institute of Mathematics Lecture 3 Math 17(Inst of Mathematics Polynomials Basic

# Lecture 3 - Polynomials Basic Operations and Factoring...

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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 .  • • • 