# Unit 5 POLYNOMIAL FUNCTIONS Unit Essential Question How

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Unit 5 POLYNOMIAL FUNCTIONS

Unit Essential Question: How are the properties of exponents and factoring going to help us solve polynomial functions?

Lesson 5. 1 PROPERTIES OF EXPONENTS

Lesson Essential Question: What are the different properties of exponents and how are they used?

Properties of Exponents: Product of Powers Power of Product Negative Exponent Zero Exponent Quotient of Powers Power of Quotient

Simplifying Expressions using Properties:

Scientific Notation:

Homework: Pages 333 – 334 #’s 3 – 39 odds, 43 – 45

Bell Work:

Classwork/Homework: Page 333 #’s 4 – 42 evens and 46 This assignment is due by the end of class!!!

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Lesson 5. 3 SIMPLIFYING POLYNOMIAL EXPRESSIONS

Lesson Essential Question: How do we simplify polynomial expressions?

Multiplying Polynomials

Homework: Pages 349 - 351 3 – 51 odds and 59 – 62

Bell Work:

Lesson 5. 4 FACTORING AND SOLVING POLYNOMIAL FUNCTIONS

Lesson Essential Question: Why is it necessary to factor a polynomial expression in order to solve the equation?

GCF

Trinomials

Factoring by Grouping

Special Factoring Patterns

Solving Polynomial Equations:

Homework: Pages 356 – 358 #’s 3 – 55 every other odd (3, 7, 11…), then 61 and 62

Bell Work:

Class Work: Pages 356 – 358 #’s 8, 10, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44, 50, 52, 58, 60 This assignment will be collected tomorrow!

Bell Work:

Quiz Tomorrow: Properties of Exponents Scientific Notation Factoring Polynomial Expressions Solving Polynomial Functions

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Lesson 5. 5 DIVISION OF POLYNOMIALS

Lesson Essential Question: What are the two ways we can divide polynomials and how do we use the remainder/factor theorem? ? ?

Long Division of Polynomials

Remainders!!!

Homework: Page 366 #’s 3 – 10

Bell Work:

Example:

Synthetic Division:

Remainders!!!

Homework: Page 366 #’s 11 – 18

Bell Work:

Remainder Theorem: When using synthetic division, the remainder that you get when you divide f(x) by some binomial (x – c) is the same value that you would get if you evaluated f(c). This is easier shown by examples.

Factor Theorem: If the remainder you get when you use synthetic or long division is zero, this means that the original divisor you used is an actual factor for the polynomial. Why does this help us? ? ?

This problem is CRAZY GOOD…

Example:

Example:

Homework: Pages 366 - 367 #’s 21 – 39 odds, and two word problems 41 and 42!!! This assignment will be collected!

Bell Work: Be ready to go over last night’s homework!!!

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Lesson 5. 6 FINDING RATIONAL ZEROS

Lesson Essential Question: How do we find all possible rational zeros for a function if it will not factor and we do not know any prior information about the function?

Rational Zero Theorem:

Or… Use your graphing calculator to estimate where a zero might be, then test it using the factor theorem!!!

Examples:

Bell Work:

Homework: Pages 374 - 376 #’s 11 – 17 odds, 25, 29, 33, 45 Find ALL ZEROS for these (this is includes complex and irrational zeros)!!! For 11 – 17 odds, sketch the graph and find the intervals at which f(x) > 0 and f(x) < 0.

Bell Work:

Classwork/Homework: Pages 374 - 375 #’s 12 – 18 evens and 28 – 34 evens 46, and 51 Find ALL ZEROS for these (this is includes complex and irrational zeros)!!! For 12 – 18, find the intervals at which f(x) < 0 and f(x) > 0. This will be collected!!!

Pop Quiz:

Test Upcoming!!! Test will be on: Factoring Long Division Synthetic Division Remainder/Factor Theorem Rewriting Polynomials in Factored Form Finding ALL Zeros for a Polynomial Function

Review:

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Review:

Bell Work: You have been charged with building the base of a statue that will consist of three rectangular blocks. The three blocks have the same height of x, and the base of each block is to be a square. The bottom block will have sides of (8 x + 16), and each block above it will be half of the previous. The volume of the three cement blocks is to be 67, 200 cubic inches. Find the dimensions of each block.

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