Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min)...

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Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up: 1. What do you need to combine like terms 2. x + x = 3. x 2 + x 2 = 4. 3x 2 + 5x 2 = 5. -4x – 3x = 6. 3x 3 + 5x 3 = HW#5: Adding & Subtracting Polynomials

Transcript of Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min)...

Page 1: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Wed, 3/23SWBAT…add and subtract polynomials

Agenda

1. Adding & subtracting polynomials (10 min)

2. Multiplying a monomial by a polynomial (10 min)

Warm-Up:

1. What do you need to combine like terms?

2. x + x =

3. x2 + x2 =

4. 3x2 + 5x2 =

5. -4x – 3x =

6. 3x3 + 5x3 =

HW#5: Adding & Subtracting Polynomials

Page 2: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

A term is either a single number or a variable, or numbers and variables multiplied together.

A monomial is one term A binomial is the sum or difference of two monomials A trinomial is the sum or difference of three monomials A polynomial is a monomial or the sum or difference of

monomials (not division)

Page 3: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Polynomials in Standard Form The standard form of a polynomial is written with

the terms in order from greatest degree to least degree.

Ex1: 3x2 – 4x5 – 7xAnswer: -4x5 + 3x2 – 7xThe leading coefficient is 4

Ex2: 5y + 9 – 2y4 – 6y3

Answer: -2y4 – 6y3 + 5y + 9The leading coefficient is -2

Page 4: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Reminder!Reminder! Like terms have:

The same variable ANDThe same exponent

When combining like terms, add or subtract the numbers, but DO NOT touch the exponents!For example, 6a + 4a = 10aFor example, 6c2 – 4c2 = 2c2

Page 5: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Adding polynomials

Find each sum and arrange in standard form:

1. (3x2 + 5) + (5x2 + 7)

2. (2x2 – 4x + 3) + (x2 – 3x + 1)

Page 6: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Adding polynomials

Find each sum and arrange in standard form:

1. (3x2 + 5) + (5x2 + 7) = 8x2 + 12

2. (2x2 – 4x + 3) + (x2 – 3x + 1) = 3x2 – 7x + 4

Page 7: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Subtracting polynomials

Find each difference and arrange in standard form:

1. (6c2 + 5c – 3) – (4c2 + c)

2. (5y4 + 3y3 – 10y + 3) – (5y3 + y2 + 7)

Page 8: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Mon, 3/12 SWBAT…add & subtract polynomials and multiply a monomial by a polynomial

Agenda

1. WU (15 min)

2. Work on HW#5 (15 min)

3. Exit slip: (5 min)

Warm-Up:

1.) For the polynomial: x2 + 1, name the:

a.) Terms

b.) Degree

c.) Function name

Find the difference & arrange in standard form:

2.) (4y4 + 3y3 + 11y + 3) – (7y3 + 4y2 + 2)

3.) (8x2 + 7x – 5) – (3x2 – 4x) – (-6x3 – 5x2 + 3)

HW#5: Polynomials

Page 9: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Adding and Subtracting Polynomials:

Find the difference & arrange in standard form:

2.) (4y4 + 3y3 + 11y + 3) – (7y3 + 4y2 + 2)

4y4 + 3y3 + 11y + 3 – 7y3 – 4y2 – 2

Answer: 4y4 – 4y3 – 4y2 + 11y + 1

3.) (8x2 + 7x – 5) – (3x2 – 4x) – (-6x3 – 5x2 + 3)

Answer: 6x3 + 10x2 + 4y2 + 11x – 8

Page 10: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Properties of Polynomials:

Use the polynomial 3x – x2 + 1 to answer questions a – g:

a.How many terms does the polynomial have?

b.List the three terms:

c.What is the degree of the polynomial?

d.Write the polynomial in standard form:

e.What is the leading coefficient?

f.What is the name of the function?

g.What is the graph called?

Page 11: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Multiplying a Monomial with a Polynomial:

Find the product & arrange in standard form:

4.) 9x²(6x4 – 2x³ + 3x² – x)

Answer: 54x6 –18x5 + 27x4 – 9x3

5.) -xy(x6 – x3 – xy)

Answer: -x7y + x4y + x2y2

Page 12: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Solving Equations with Polynomials:

Solve each equation:

6.) 2k(-3k + 4) + 6(k2 + 10) = k(4k + 8) – 2k(2k + 5)

k = -6

7.) 9c(c – 11) + 10(5c – 3) = 3c(c + 5) + c(6c – 3) – 30

c = 0

Page 13: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Work on HW#5

Page 14: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Exit Slip: Complete on a ½ sheet

1. Simplify: -x(x3 – x2)

2. Simplify: 9b²(2b³ – 3b² + b)

3. Solve: 7(2w2 + 8w – 3) + 13 = 2(7w2 + 6w + 7)

Page 15: Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

HW#5 Answers

1.) 8x2 + 12

2.) 3x2 – 7x + 4

3.) 2c2 + c – 3

4.) 3x2 + 3x – 20

5.) -2y3 – y2 – 11y + 1

6.) 3n2 – n – 4


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