# A.A B.B C.C D.D 5-Minute Check 1. A.A B.B C.C D.D 5-Minute Check 2.

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A.A B.B C.C D.D 5-Minute Check 1

A.A B.B C.C D.D 5-Minute Check 2

A.A B.B C.C D.D 5-Minute Check 3

A.A B.B C.C D.D 5-Minute Check 4

A.A B.B C.C D.D 5-Minute Check 6

Example 1 Multiply a Polynomial by a Monomial Horizontal Method Find 6y(4y 2 – 9y – 7). 6y(4y 2 – 9y – 7)Original expression = 6y(4y 2 ) – 6y(9y) – 6y(7)Distributive Property = 24y 3 – 54y 2 – 42yMultiply.

Example 1 Multiply a Polynomial by a Monomial Vertical Method Answer: 24y 3 – 54y 2 – 42y 4y 2 – 9y – 7 (×) 6yDistributive Property 24y 3 – 54y 2 – 42yMultiply.

A.A B.B C.C D.D Example 1 A.6x 2 + 9x + 15 B.6x 3 + 9x 2 + 15x C.5x 3 + 6x 2 + 8x D.6x 2 + 3x + 5 Find 3x(2x 2 + 3x + 5).

Example 2 Simplify Expressions Simplify 3(2t 2 – 4t – 15) + 6t(5t + 2). 3(2t 2 – 4t – 15) + 6t(5t + 2) = 3(2t 2 ) – 3(4t) – 3(15) + 6t(5t) + 6t(2)Distributive Property = 6t 2 – 12t – 45 + 30t 2 + 12tProduct of Powers = (6t 2 + 30t 2 ) + [(– 12t) + 12t] – 45Commutative and Associative Properties = 36t 2 – 45Combine like terms. Answer: 36t 2 – 45

A.A B.B C.C D.D Example 2 A.4y 2 + 9y + 1 B.8y 2 + 5y – 6 C.20y 2 + 9y + 6 D.28y 2 + 31y – 10 Simplify 5(4y 2 + 5y – 2) + 2y(4y + 3).

Example 3 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. Read the Test Item The question is asking you to find the total cost if Wyome rode 9 super rides, in addition to the regular rides, and park admission.

Example 3 Solve the Test Item Write an equation to represent the total money Wyome spent. Let C represent the total cost of the day. C= 3s + 2(15 – s) + 10total cost = 3(9) + 2(15 – 9) + 10Substitute 9 in for s. = 3(9) + 2(6) + 10Subtract 9 from 15. = 27 + 12 + 10Multiply. = 49Add.

Example 3 Answer: It cost \$49 to ride 9 super rides, 6 regular rides, and admission.

A.A B.B C.C D.D Example 3 A.\$120,000 B.\$21,200 C.\$70,000 D.\$210,000 The Fosters own a vacation home that they rent throughout the year. The rental rate during peak season is \$120 per day and the rate during the off-peak season is \$70 per day. Last year they rented the house 210 days, p of which were during peak season. Determine how much rent the Fosters received if p is equal to 130.

Example 4 Equations with Polynomials on Both Sides Solve b(12 + b) – 7 = 2b + b(–4 + b). b(12 + b) – 7= 2b + b(–4 + b)Original equation 12b + b 2 – 7= 2b – 4b + b 2 Distributive Property 12b + b 2 – 7= –2b + b 2 Combine like terms. 12b – 7= –2bSubtract b 2 from each side.

Example 4 Equations with Polynomials on Both Sides 12b = –2b + 7Add 7 to each side. Divide each side by 14. Answer: 14b = 7Add 2b to each side.

Example 4 Equations with Polynomials on Both Sides Check b(12 + b) – 7 = 2b + b(–4 + b) Original equation Simplify. Multiply. Subtract.

A.A B.B C.C D.D Example 4 Solve x(x + 2) + 2x(x – 3) + 7 = 3x(x – 5) – 12. A. B. C. D.

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