Warm–up #4. Warm–up #4 Solutions Homework Log Wed 9/9 Lesson 1 – 4 Learning Objective: To add, subtract, & multiply polynomials Hw: #105 Pg. 36 #1 –

Warm–up #41. Simplify

Warm–up #4 Solutions1.=

Homework LogWed

9/9

Lesson 1 – 4

Learning Objective: To add, subtract, & multiply polynomials

Hw: #105 Pg. 36 #1 – 8 all, 9 – 61 eoo

9/9/15 Lesson 1 – 4 Polynomials

Advanced Math/Trig

Learning Objective

To add polynomials

To subtract polynomials

To multiply polynomials

To name polynomials

PolynomialsDegree of Term – sum of exponents on variables

Degree of Polynomial – largest degree among terms

Monomial – one term

Binomial – two terms

Trinomial – three terms

PolynomialsPolynomial096x – 2

– 4+ 5 + 38y

Degree Typenone monomial0 monomial1 (linear) binomial2 (quadratic)trinomial3 (cubic) binomial4 (quartic) trinomial5 (quantic) binomial

Adding & Subtracting Polynomials

1. 3 3(4 8 7) (5 3 6)x x x x Combine like terms

39 5 1x x

2. 6 2 2(6 9 5 ) (11 3 8)x x x x x Distribute (–) sign

6 2 26 9 5 11 3 8x x x x x

6 26 2 2 8x x x

cubic trinomial

degree 6 polynomial

Multiplying Polynomials

2 2(2 5 3)(4 3 )x x x x 3. 4 3 3 2 28 6 20 15 12 9x x x x x x

distribute

( 2)(4 3)x x 4. F irstO uterI nnerL ast

24 3 8 6x x x 24 11 6x x

4 3 28 14 27 9x x x x quartic poly

quadratic trinomial

Multiplying Polynomials

2

2

(5 2)(3 4)

15 20 6 8

15 14 8

n n

n n n

n n

x x

x x x

x x

5.

F irstO uterI nnerL ast

unknown degree trinomial

Box Method6. (3x – y)(x + 2y)

3

– y 3x

–xy 3

–26xy

x

2y

Vertical Method

4 2 2(3 2 )( 2 4)x x x x x 4 2

2

4 2

5 3 2

6 4 3

6 5 4 3 2

3 22 4

12 8 46 4 2

3 23 6 14 5 6 4

x x xx x

x x xx x x

x x xx x x x x x

degree 6 poly

7.

Box Method8. (x – 4)(2

2

3 2

–12–8

x

– 4

3 2 – 1

–x

4

Box Method9. ( – 3x + 1)(2

4

6 4

–9–6

2

–3x

3 2 – 1

–2

3x

2 3x –1 1

Special Product RulesDifference of two squares

(x – y)(x + y) =

Square of a binomial

Special Product RulesCube of a binomial

Special Product RulesSum of two cubes

Difference of two cubes

Multiply9. (3x – (3x +

Difference of Squares

9

Quartic Binomial

Multiply10. = (3x + 4)(3x + 4)

Square of a binomial

9

Quadratic Trinomial

Multiply11.

Square of a binomial

25

Degree 6 Trinomial

Multiply12.

Cube of a binomial

Cubic Polynomial

Multiply13. + 2xy + 4

Difference of two cubes

Cubic Binomial

Ticket Out the Door

Express without absolute values if x < 2

Explain how you came up with your answer

Homework#105 Pg. 36 1 – 8 all, 9 – 63

odd &

name answer by degree & # of terms