6.1 Review of the Rules for Exponents Product rule for exponents: Power Rule (a) for exponents: Power Rule (b) for exponents: Power Rule (c) for exponents:

6.1 Review of the Rules for Exponents Changing from negative to positive exponents: Quotient rule for exponents:

6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials When you read a sentence, it split up into words. There is a space between each word. Likewise, a mathematical expression is split up into terms by the +/- sign: A term is a number, a variable, or a product or quotient of numbers and variables raised to powers.

6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials Like terms – terms that have exactly the same variables with exactly the same exponents are like terms: To add or subtract polynomials, add or subtract the like terms.

6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials Degree of a term – sum of the exponents on the variables Degree of a polynomial – highest degree of any non-zero term

6.2 Adding and Subtracting Polynomials; Graphing Simple Polynomials Monomial – polynomial with one term Binomial - polynomial with two terms Trinomial – polynomial with three terms Polynomial in x – a term or sum of terms of the form

6.3 Multiplication of Polynomials Multiplying a monomial and a polynomial: use the distributive property to find each product. Example:

6.3 Multiplication of Polynomials Multiplying two polynomials:

6.3 Multiplication of Polynomials Multiplying binomials using FOIL (First – Inner – Outer - Last): F – multiply the first 2 terms O – multiply the outer 2 terms I – multiply the inner 2 terms L – multiply the last 2 terms Combine like terms

6.3 Multiplication of Polynomials Squaring binomials: Examples:

6.3 Multiplication of Polynomials Product of the sum and difference of 2 terms: Example:

6.4 Division of Polynomials Dividing a polynomial by a monomial: divide each term by the monomial

6.4 Division of Polynomials Dividing a polynomial by a polynomial:

6.4 Division of Polynomials Synthetic division: answer is: remainder is: -1