246)

1654) 3

ba

Warm-Up: September 18/21, 2015 Simplify

Homework Questions?

If you do not have the correct units, your answer is wrong.

P.3 Even Answers

dayin

61)106

s52)104

Diagnostic Test Results

Below 10 – You may not be ready for this course.◦ You may want to consider speaking with your

counselor about an alternate placement.◦ If you stay in this course, you will likely need extra

help. Mr. Szwast is available almost every day during lunch and after school.

10-20 – You are probably in the right course, but may need to complete some extra review

Above 20 – You are most likely prepared for this course, and might do well in honors.◦ There may not be any open spots in honors.

Diagnostic Test Results

Polynomials Section P.4

Understand the vocabulary of polynomials

Add and subtract polynomials Multiply polynomials Use FOIL in polynomial multiplication Use special products in polynomial

multiplication Perform operations with polynomials in

several variables

Objectives

If a ≠ 0, the degree of axn is n. The degree of a nonzero constant is 0. Degree ≈ Exponent of variable

The Degree of axn

A polynomial in x is an algebraic expression of the (standard) formanxn + an-1xn-1 + an-2xn-2 + … + a1x + a0

Coefficients an, an-1, an-2, …, a1 and a0 are real numbers.

an ≠ 0, and n is a natural number. The polynomial is of degree n, an is the leading coefficient a0 is the constant term.

Definition of a Polynomial in x

Example 1: Write in Standard Form 4757234 2323 xxxxxx

You-Try #1: Write in Standard Form 682133579 2323 xxxxxx

542732 2324 xxxxxx

Example 2: Simplify and Write in Standard Form

Use the Distributive Property Multiply each term of one polynomial by

each term of the other polynomial. Then combine like terms.

The box method is a great way to keep your work organized.

Multiplying Polynomials when Neither is a Monomial

45524 22 xxxx

You-Try #2: Simplify andWrite in Standard Form

Warm-Up: September 21, 2015Write in Standard Form

35432)

2432)23

xxxxb

xxa

Homework Questions?

Multiplying Binomials - FOIL

(ax + b)(cx + d) = ax · cx + ax · d + b · cx + b · d

firstlast

inner

outer

•First•Outer•Inner•Last

Let A and B represent real numbers, variables, or algebraic expressions. 

Special Products

(A B)(A B) A2 B2

(A B)2 A2 2AB B2

(A B)2 A2 2AB B2

275275 yxyx

Example 5: Multiply and Simplify

You-Try #5: Multiply and Simplify

243243 yxyx

Degree Name Examplen=0 Constant -7n=1 Linear 2x+8n=2 Quadratic x2+5x-7n=3 Cubic 5x3-9xn=4 Quartic 9x4-2x3+3x2-x+4n=5 Quintic -3x5

Half-Name Based on Degree

Monomial: One term Binomial: Two terms; the sum of two

monomials Trinomial: Three terms; the sum of three

monomials Polynomial: One or more terms; the

sum of one or more monomials. Used in name if more than three terms.

Half-Name Based on # Terms(In Standard Form)

Name the following polynomials based on their degree and number of terms.

You-Try #6

253

4

2

3

7273)

2)

217)

45)

xxxxd

xc

xxb

xxa

Read Section P.4 Page 41 #1-73 EOO, 87-93 odd

Quiz on P.1-P.4 soon

Assignment

In Exercises 15-58, find each product

In Exercises 59-82, find each product.

87) The polynomial 0.018x2-0.757x+9.047 describes the amount, in thousands of dollars, that a person earning x dollars feels underpaid. Evaluate the polynomial for x=40. Describe what the answer means in practical terms.

33)73

)69

57)65

723)61

22

2

yxyxyxyxyx

yx

yxyx