name:__________ warm-up 8-1 determine whether –8 is a polynomial. if so, identify it as a...

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Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would represent the area of the shaded region? What is the degree of the polynomial 5ab 3 + 4a 2 b + 3b 5 – 2? Which of the following polynomials is a cubic trinomial? A. –2x 4 + 5x 2 B. 4g 3 – 8g 2 + 6 C. 7w 2 + 12 – 5w 4 D. 16 – 3p + 9p 2

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Page 1: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Name:__________ warm-up 8-1

Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial

Give a polynomial that would represent the area of the shaded region?

What is the degree of the polynomial 5ab3 + 4a2b + 3b5 – 2?

Which of the following polynomials is a cubic trinomial?A. –2x4 + 5x2

B. 4g3 – 8g2 + 6

C. 7w2 + 12 – 5w4

D. 16 – 3p + 9p2

Page 2: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Definition of polynomial:

An expression that can have constants, variables and exponents, but:

* no division by a variable.* a variable's exponents can only be 0,1,2,3,... etc.* it can't have an infinite number of terms.

Page 3: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Details of the DayEQ:When could a non-linear function be used to represent a real world situation?

I will be able to…

Activities:Warm-upReview homeworkNotes: 8-1: Adding and Subtracting polynomials8-2: Multiply a polynomial by a monomialClass work/ HW

Vocabulary:•binomial

•trinomial

•degree of a monomial

•degree of a polynomial

•standard form of a polynomial

•leading coefficient

.

• Solve equations involving the products of monomials and polynomials

• Write polynomials in standard form.• Add and subtract polynomials.• Multiply a polynomial by a monomial.

.

Page 4: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

8-1 ADDING AND SUBTRACTION POLYNOMIALS

Exponential FunctionsPolynomialsPolynomialsPolynomialsPolyno

mials PolynomialsPolynomialsPolynomialsPolynomialsPolynomialsPolynomials PolynomialsPolynomialsPolynomialsPolynomialsPolynomialsPolynomialsPolynomialsPolynomials

8-2 Multiplying a Polynomial by a Monomial

Page 5: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

A Quick Review Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial

Give a polynomial that would represent the area of the shaded region?

What is the degree of the polynomial 5ab3 + 4a2b + 3b5 – 2?

Which of the following polynomials is a cubic trinomial?A. –2x4 + 5x2

B. 4g3 – 8g2 + 6

C. 7w2 + 12 – 5w4

D. 16 – 3p + 9p2

Page 6: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesState whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial

An expression that can have constants, variables and exponents, but:

* no division by a variable.* a variable's exponents can only be 0,1,2,3,... etc.* it can't have an infinite number of terms.

Page 7: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesA. State whether 3x2 + 2y + z is a polynomial. If it is a polynomial, find the degree and identify it as a monomial, binomial, or trinomial.

B. State whether 4a2 – b–2 is a polynomial. If it is a polynomial, find the degree and identify it as a monomial, binomial, or trinomial.

C. State whether 8r – 5s is a polynomial. If it is a polynomial, find the degree and identify it as a monomial, binomial, or trinomial

D. State whether 3y5 is a polynomial. If it is a polynomial, find the degree and identify it as a monomial, binomial, or trinomial.

Page 8: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesA. Write 9x2 + 3x6 – 4x in standard form. Identify the leading coefficient.

B. Write 12 + 5y + 6xy + 8xy2 in standard form. Identify the leading coefficient.

A. Write –34x + 9x4 + 3x7 – 4x2 in standard form

B. Identify the leading coefficient of 5m + 21 –6mn + 8mn3 – 72n3 when it is written in standard form.

Page 9: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesFind (7y2 + 2y – 3) + (2 – 4y + 5y2).Using horizontal method

Using vertical method

B. Find (4x2 – 2x + 7) + (3x – 7x2 – 9). Find (3x2 + 2x – 1) + (–5x2 + 3x + 4).

Page 10: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesB. Find (4x3 + 2x2 – x + 2) + (3x2 + 4x – 8). Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2).

Find (6n2 + 11n3 + 2n) – (4n – 3 + 5n2). . Find (3x3 + 2x2 – x4) – (x2 + 5x3 – 2x4).

Page 11: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesFind (8y4 + 3y2 – 2) – (6y4 + 5y3 + 9). R = 0.46n3 – 1.9n2 + 3n + 19

T = 0.45n3 – 1.85n2 + 4.4n + 22.6A. Write an equation that represents the

sales of video games V.

A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of traditional toys R. In recent years, the sales of traditional toys and total sales could be modeled by the following equations, where n is the number of years since 2000.

B. Use the equation to predict the amount of video game sales in the year 2012.

Page 12: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examplesA. BUSINESS The profit a business makes is found by subtracting the cost to produce an item C from the amount earned in sales S. The cost to produce and the sales amount could be modeled by the following equations, where x is the number of items produced.C = 100x2 + 500x – 300S = 150x2 + 450x + 200Find an equation that models the profit.

B. Use the equation 50x2 – 50x + 500 to predict the profit if 30 items are produced and sold.

Page 13: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examples Find 6y(4y2 – 9y – 7). Find 3x(2x2 + 3x + 5).

Simplify 3(2t2 – 4t – 15) + 6t(5t + 2). Simplify 5(4y2 + 5y – 2) + 2y(4y + 3).

Page 14: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examples GRIDDED RESPONSE Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each and regular rides are an additional $2. Wyome goes to the park and rides 15 rides, of which s of those 15 are super rides. Find the cost if Wyome rode 9 super rides.

Solve b(12 + b) – 7 = 2b + b(–4 + b).

Page 15: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examples Solve x(x + 2) + 2x(x – 3) + 7 = 3x(x – 5) – 12.

Page 16: Name:__________ warm-up 8-1 Determine whether –8 is a polynomial. If so, identify it as a monomial, binomial, or trinomial Give a polynomial that would

Notes and examples