1. Lesson 5 Menu Five-Minute Check (over Lesson 7-4) Main Ideas Targeted TEKS Example 1: Multiply a Polynomial by a Monomial Example 2: Simplify Expressions Example 3: Real-World Example Example 4: Polynomials on Both Sides

2. Lesson 5 MI/Vocab Find the product of a monomial and a polynomial. Solve equations involving polynomials.

3. Lesson 5 Ex1 Multiply a Polynomial by a Monomial Method 1 Horizontal Find 6y(4y 2 – 9y – 7). 6y(4y 2 – 9y – 7) = 6y(4y 2 ) – 6y(9y) – 6y(7)Distributive Property = 24y 3 – 54y 2 – 42yMultiply.

4. Lesson 5 Ex1 Multiply a Polynomial by a Monomial Method 2 Vertical Answer: 24y 3 – 54y 2 – 42y 4y 2 – 9y – 7 (x) 6yDistributive Property 24y 3 – 54y 2 – 42yMultiply.

5. A.A B.B C.C D.D Lesson 5 CYP1 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).

6. Lesson 5 Ex2 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 Answer: = 36t 2 – 45Combine like terms.

7. Lesson 5 CYP2 1.A 2.B 3.C 4.D 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).

8. Lesson 5 Ex3 A. ENTERTAINMENT 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. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. Find an expression for how much money Sarita spent at the park. Words VariableIf s = the number of super rides, then 15 – s is the number of regular rides. Let M be the amount of money Sarita spent at the park. Amount of moneyequals admissionplus super rides times $3 per ride plus regular rides times $2 per ride.

9. Lesson 5 Ex3 EquationM = 10 + s ● 3 + (15 – s) ● 2 = 10 +3s + 15(2) – s(2)Distributive Property = 10 + 3s + 30 – 2sSimplify. = 40 + sSimplify. Answer: An expression for the amount of money Sarita spent in the park is 40 + s, where s is the number of super rides she rode.

10. Lesson 5 Ex3 B. Evaluate the expression to find the cost if Sarita rode 9 super rides. 40 + s = 40 + 9s = 9 = 49Add. Answer: Sarita spent $49.

11. 1.A 2.B 3.C 4.D Lesson 5 CYP3 A.70p + 210 B.120p + 70 C.50p + 14,700 D.70p + 120 A. 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. Find an expression for how much rent the Fosters received.

12. 1.A 2.B 3.C 4.D Lesson 5 CYP3 A.$120,000 B.$21,200 C. $70,000 D.$210,000 B. Evaluate the expression if p is equal to 130.

13. Lesson 5 Ex4 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. Polynomials on Both Sides

14. Lesson 5 Ex4 12b = –2b + 7Add 7 to each side. Divide each side by 14. Answer: Polynomials on Both Sides 14b = 7Add 2b to each side.

15. Lesson 5 Ex4 Check b(12 + b) – 7 = 2b + b(–4 + b) Original equation Simplify. Polynomials on Both Sides Multiply. Subtract.

16. A.A B.B C.C D.D Lesson 5 CYP4 Solve x(x + 2) + 2x(x – 3) + 7 = 3x(x – 5) – 12. A. B. C. D.