PSAE Chapter 5 Review: Student Edition Name: _______________________  Take NOTES in the spaces provided 

Section 5.1: What are polynomials? Here’s a polynomial: Each one of the little blobs is a “term:” “Poly” means “many” One term = _________________________________ Two terms = ________________________________ Three terms = _______________________________ Four terms = ________________________________

Section 5.1: How to find Degree 1.Look at the terms…. 2.Whichever term has the MOST letters wins! (after you simplify) What is the degree of the following:

5.1: SIMPLIFYING a Polynomial Do not confuse with “__________________!” Simply GROUP like terms: Ex:

5.1: Descending versus Ascending Descending Order Powers of the variables… ___________________ ___________________ ___________________ ____________ AKA: “________________” Ex: ____________ Powers of the variables… ___________________ ___________________ ___________________ ____________ AKA: “________________” Ex: ____________ Ascending Order Powers of the variables… ___________________ ___________________ ___________________ ____________ Ex: ____________ Powers of the variables… ___________________ ___________________ ___________________ ____________ Ex: ____________

5.1: Classifying Polynomials Classifying Polynomials by Number of Terms # of TermsClassificationExamples m, n 5, xy, -5ab 2, r 2 st 3, 9 3x + 4y, jk – 3, a 2 + 7a r + s – t, a 2 + 2a - 6

5.1: Classifying Polynomials Which phrase best describes –z 3 + 3z 2 – 2z – 3z 2 ? – First, simplify…. – How many terms are left? – What is the greatest degree of the terms? – The correct choice is ________________________________ Classifying Polynomials by Degree DegreeClassificationExamples X, -6d, 5s – 3, 7 + 8y x 2, 3m 2, k – k 2, 4 – 2g + 6g X 3, -8b 3, 4b 3 – b2

5.1: Adding & Subtracting Adding Polynomials GROUP like terms Ex: (3x 2 + x 2 – 3) + (4x 3 + 2x 2 + 5x) GROUP like terms Ex: (3x 2 + x 2 – 3) + (4x 3 + 2x 2 + 5x) Subtracting Polynomials Find the “additive inverse” first (AKA: take the OPPOSITE!) Then, GROUP like terms just like adding Ex: (3c 2 – 8c + 4) – (7 + c 2 – 8c) Find the “additive inverse” first (AKA: take the OPPOSITE!) Then, GROUP like terms just like adding Ex: (3c 2 – 8c + 4) – (7 + c 2 – 8c)

5.1: One last thing…. What do you do when the problem says: Find the difference when x – 2x is subtracted from 2x – 10x 2 + 7?

5.2: Properties of Exponents Multiplication Properties Division Properties

5.2 Properties of Exponents NEVER leave negative exponents in your answers!

5.2: Scientific Notation a x 10 n  Scientific Notation – a can be _______ – a cannot be _________ – a must be bigger than _____, smaller than _____! n can be ______________ or ______________

5.2: Scientific Notation Is the number written in scientific notation? x __________ 24 x 10 5 __________ 6 x __________ x 10 2 __________ 10 x 5 2 __________

5.2: Multiplying & Dividing Scientific Notation Simplify: