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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 C. 7w – 5w 4 D. 16 – 3p + 9p 2

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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.

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Details of the Day EQ: When could a non-linear function be used to represent a real world situation? I will be able to… Activities: Warm-up Review homework Notes: 8-1: Adding and Subtracting polynomials 8-2: Multiply a polynomial by a monomial Class 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..

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Exponential Functions PolynomialsPolynomialsPolynomialsPolynomials PolynomialsPolynomials PolynomialsPolynomials 8-2 Multiplying a Polynomial by a Monomial

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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 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 C. 7w – 5w 4 D. 16 – 3p + 9p 2

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Notes and examples State 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.

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Notes and examples A. State whether 3x 2 + 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 4a 2 – 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 3y 5 is a polynomial. If it is a polynomial, find the degree and identify it as a monomial, binomial, or trinomial.

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Notes and examples A. Write 9x 2 + 3x 6 – 4x in standard form. Identify the leading coefficient. B. Write y + 6xy + 8xy 2 in standard form. Identify the leading coefficient. A. Write –34x + 9x 4 + 3x 7 – 4x 2 in standard form B. Identify the leading coefficient of 5m + 21 –6mn + 8mn 3 – 72n 3 when it is written in standard form.

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Notes and examples Find (7y 2 + 2y – 3) + (2 – 4y + 5y 2 ). Using horizontal method Using vertical method B. Find (4x 2 – 2x + 7) + (3x – 7x 2 – 9).Find (3x 2 + 2x – 1) + (–5x 2 + 3x + 4).

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Notes and examples B. Find (4x 3 + 2x 2 – x + 2) + (3x 2 + 4x – 8). Find (6y 2 + 8y 4 – 5y) – (9y 4 – 7y + 2y 2 ). Find (6n n 3 + 2n) – (4n – 3 + 5n 2 ).. Find (3x 3 + 2x 2 – x 4 ) – (x 2 + 5x 3 – 2x 4 ).

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Notes and examples Find (8y 4 + 3y 2 – 2) – (6y 4 + 5y 3 + 9). R = 0.46n 3 – 1.9n 2 + 3n + 19 T = 0.45n 3 – 1.85n n A.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 B. Use the equation to predict the amount of video game sales in the year 2012.

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Notes and examples A. 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 = 100x x – 300 S = 150x x Find an equation that models the profit. B. Use the equation 50x 2 – 50x to predict the profit if 30 items are produced and sold.

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Notes and examples Find 6y(4y 2 – 9y – 7).Find 3x(2x 2 + 3x + 5). Simplify 3(2t 2 – 4t – 15) + 6t(5t + 2).Simplify 5(4y 2 + 5y – 2) + 2y(4y + 3).

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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).

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

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Notes and examples

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