College Algebra & Trig Home Page - Battaly's Home Page · College Algebra & Trig Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Homework Problems P.4 Polynomials

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 1

January 30, 2016

P.4 Polynomials

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Study P.4 CVC # 1 ­ 13; #1­7; 9, 13, 17, ... 53 59, 63, 67, 71, 75, 79, 85, 87

Homework Problems

College Algebra & Trig Home Page

GOALS:1. Perform operation of addition, subtraction and multiplication of polynomials.2. Review FOIL in mult of polynomials3. Recognize and perform special products

2x2y

Monomial: product of a constant and one or more variables raised to whole number powers

Polynomial: monomial or sum of monomials

Degree: Exponent: for term with one variableSum of Exponents: for term with more than one variableDegree of Polynomial: Highest degree of any term

3

2a2

y2 5b2c

7z

2x2y + 3x ­ 2xy + 9

top: left to right0, 2, 2, 3, 1, 3

polynomial above: 3

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework ProblemsCollege Algebra & Trig Home Page

P.4 Polynomials

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 2

January 30, 2016

2x2 y

Term: product of a constant and one or more variables

3 2a1/3

y2 7z

4x2 ­ 7x + 5x2 + 9x

b1/2 Like Terms: have same variables to same exponents

3x ­ x1/2 Polynomial?

Which are "like terms"?

Simplify

How many terms?

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

9x2 + 2x

College Algebra & Trig Home Page

P.4 Polynomials

2x2 y

Term: product of a constant and one or more variables

3 2a1/3

y2 7z

4x2 ­ 7x + 5x2 + 9x

b1/2 Like Terms: have same variables to same exponents

3x ­ x1/2 Polynomial?

Which are "like terms"?

Simplify

How many terms?

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

9x2 + 2x

College Algebra & Trig Home Page

P.4 Polynomials

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 3

January 30, 2016

Simplify ­5x3 ­ 8x2 + 4 ­ 4x3 +x ­ 9

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

­9x3 ­ 8x2 + x ­ 5

College Algebra & Trig Home Page

P.4 Polynomials

Simplify ­5x3 ­ 8x2 + 4 ­ 4x3 +x ­ 9

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

­9x3 ­ 8x2 + x ­ 5

College Algebra & Trig Home Page

P.4 Polynomials

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 4

January 30, 2016

Simplify(x3y ­ 5x2y2 + 2xy3) + (5x2y2 ­ 4xy3 + 7y4)

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

x3y ­ 2xy3 + 7y4

College Algebra & Trig Home Page

P.4 Polynomials

x3y ­ 5x2y2 + 2xy3 + 5x2y2 ­ 4xy3 + 7y4

Simplify(x3y ­ 5x2y2 + 2xy3) + (5x2y2 ­ 4xy3 + 7y4)

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

x3y ­ 2xy3 + 7y4

College Algebra & Trig Home Page

P.4 Polynomials

x3y ­ 5x2y2 + 2xy3 + 5x2y2 ­ 4xy3 + 7y4

x3y ­ 2xy3 + 7y4

correctly remove parenthesis

combine like terms (CLT)

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 5

January 30, 2016

Simplify

(a3b ­ 5a2b2 + ab3) ­ (5a2b2 ­ 7ab3 + b3)

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

a3b ­ 10a2b2 + 8ab3 ­ b3

College Algebra & Trig Home Page

P.4 Polynomials

Simplify

(a3b ­ 5a2b2 + ab3) ­ (5a2b2 ­ 7ab3 + b3)

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

a3b ­ 10a2b2 + 8ab3 ­ b3

College Algebra & Trig Home Page

P.4 Polynomials

a3b ­ 5a2b2 + ab3 ­ 5a2b2 + 7ab3 ­ b3

a3b ­ 10a2b2 + 8ab3 ­ b3

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 6

January 30, 2016

Simplify(6x4y + x3y2 ­ 3x2y3) ­ (4x3y2 ­ 3x2y3 ­ 5xy4)

6x4y + x3y2 ­ 3x2y3

4x3y2 ­ 3x2y3 ­ 5xy4++

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

6x4y ­ 3x3y2 + 5xy4

P.4 Polynomials

Simplify

(6x4y + x3y2 ­ 3x2y3) ­ (4x3y2 ­ 3x2y3 ­ 5xy4)

6x4y + x3y2 ­ 3x2y3

4x3y2 ­ 3x2y3 ­ 5xy4++

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

6x4y ­ 3x3y2 + 5xy4

P.4 Polynomials

6x4y ­ 3 x3y2 + 5xy4

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 7

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 PolynomialsMonomial x Monomial

(2a3 )(5a6) ­9x(4x)

(3x2 )(xy) (­4x )(­6xy)

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 PolynomialsMonomial x Monomial

(2a3 )(5a6) ­9x(4x)

(3x2 )(xy) (­4x )(­6xy)

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 8

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

2x (x + y) Monomial x Binomial

3xy (5x ­ 2y)

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

2x (x + y)

Monomial x Binomial

3xy (5x ­ 2y)

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 9

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(2x + 1)(x ­ 1)

Binomial x Binomial

(x ­ 1)(x + 3)

F O I L First Outer Inner Last

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(2x + 1)(x ­ 1)

Binomial x Binomial

(x ­ 1)(x + 3)

F O I L First Outer Inner Last

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 10

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(2x + y)(x + y)

Binomial x Binomial

(x ­ y)(x + 3y)

F O I L

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(2x + y)(x + y)

Binomial x Binomial

(x ­ y)(x + 3y)

F O I L

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 11

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

2x (x3y ­ 5x2y2 + 2xy3)

Monomial x Polyomial

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

2x (x3y ­ 5x2y2 + 2xy3)

Monomial x Polyomial

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 12

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

Special Products: ( a + b ) 2 = a2 + 2ab + b 2

(x + y)2 (2x + y)2

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

Special Products: ( a + b )2 = a2 + 2ab + b2

(x + y)2 (2x + y)2

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 13

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(x ­ y)2 (x ­ 3y)2

Special Products: ( a + b )2 = a2 + 2ab + b2

Special Products: ( a ­ b )2 = a2 ­ 2ab + b2

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

(x ­ y)2 (x ­ 3y)2

Special Products: ( a + b )2 = a2 + 2ab + b2

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 14

January 30, 2016

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

Special Products: ( a + b )( a ­ b ) = a 2 ­ b2

(2x + y)(2x ­ y) (3x + 5y)(3x ­ 5y)

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

Special Products: ( a + b )( a ­ b ) = a 2 ­ b2

(2x + y)(2x ­ y) (3x + 5y)(3x ­ 5y)

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 15

January 30, 2016

P.4 Polynomials

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

P.4 Polynomials

College Algebra & Trig Home Page

Class Notes: Prof. G. Battaly, Westchester Community College, NY

Homework Problems

Polynomials, a Review; Classnotes, G. Battaly

© G. Battaly 2016 16

January 30, 2016