4.1 The Product Rule and Power Rules for Exponents Review: PEMDAS (order of operations) – note that exponentiation is number 2. Product rule for exponents: Example:

4.1 The Product Rule and Power Rules for Exponents Power Rule (a) for exponents: Power Rule (b) for exponents: Power Rule (c) for exponents:

4.1 The Product Rule and Power Rules for Exponents A few tricky ones:

4.1 The Product Rule and Power Rules for Exponents Examples (true or false):

4.2 Integer Exponents and the Quotient Rule Definition of a zero exponent: Definition of a negative exponent:

4.2 Integer Exponents and the Quotient Rule Changing from negative to positive exponents: Quotient rule for exponents:

4.2 Integer Exponents and the Quotient Rule Examples:

4.3 An Application of Exponents: Scientific Notation Writing a number in scientific notation: Move the decimal point to the right of the first non-zero digit. Count the places you moved the decimal point. The number of places that you counted in step 2 is the exponent (without the sign) If your original number (without the sign) was smaller than 1, the exponent is negative. If it was bigger than 1, the exponent is positive

4.3 An Application of Exponents: Scientific Notation Converting to scientific notation (examples): Converting back – just undo the process:

4.3 An Application of Exponents: Scientific Notation Multiplication with scientific notation: Division with scientific notation:

4.4 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.

4.4 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.

4.4 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

4.4 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

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

4.5 Multiplication of Polynomials Multiplying two polynomials:

4.5 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

4.6 Special Products Squaring binomials: Examples:

4.6 Special Products Product of the sum and difference of 2 terms: Example:

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

4.7 Division of Polynomials Dividing a polynomial by a polynomial: