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Chapter 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest Common Factor (GCF) VIII. Factoring Trinomials IX. Solving Quadratic Equations by Factoring 1

VII. Greatest Common Factor (GCF) a polynomial is to find an equivalent expression that is a product. An equivalent expression of this type is called a factorization of the polynomial. In the last sections, we spent much time in multiplying polynomials. up coming sections we want to reverse that process and factor. 2

What are the factors of 24? What is the GCF of 24 & 32? What are the factors of 32? At this point in the course, we have use the Distributive Law for multiplication. It can also be used to factor out the GCF. 24x + 32 = 3

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1) x(3x - 2) - 8(3x - 2) 2) x(7x + 1) + (7x + 1) 7

What is the GCF? In this form, there is no common factor to factor out. There is method that could possible work, called factoring by grouping 8

Factor by Grouping. 9

VIII. Factoring Trinomials What is the pattern? 10

( )( ) "Check if O + I = bx 11

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Going back over the Pattern! What part of the multiplication does this term come from? 20

Possible Factorizations (3x - 5)(x + 1) Which one is correct? (3x - 1)(x + 5) (3x + 5)(x - 1) (3x + 1)(x - 5) 21

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Factor Completely 24

Factor Completely 25

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IX. Solving Quadratic Equations by Factoring Standard Form of a Quadratice Equation The strategy we applied to solve linear equations will NOT work on this type of equation. The Principle of Zero Products (x - 3)(x + 5) = 0 28

Note: It is difficult to see solutions while equation is in this form! Strategy to solve quadratic (or higher degree polynomial) : Set one side to zero (Write equation in standard form). : Set each factor to zero & solve. 29

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Homework Chapter 4 Part I: Exponents & Their Properties Simplify the following Expressions 33

Part II: Negative Exponents Simplify the following expressions. Your final answer should NOT include negative exponents. Part III: Scientific Notation Multiply or divide as appropriate. Write final answer in scientific notation. 34

Part IV: Polynomials For each polynomial below (a) classify it as a monomial, binomial, trinomial, or a polynomial with no special name; (b) give the degree of the polynomial; (c) determine the leading term and leading coefficient. Part V: Addition & Subtraction of Polynomials Add or Subtract as appropriate 35

Part VI: Multiplication of Polynomials Multiply the following polynomials 36

Part VII: Greatest Common Factor (GCF) Factor out the GCF from each of the following polynomials Factor the following polynomials by grouping (if possible) 37

Part VIII: Factoring Trinomials Factor the following trinomials. If it is not possible to factor the trinomial then state that it is prime 38

Part IX: Solving Quadratic Equations by Factoring Solve the following equations by factoring 39

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