10.4 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Learn the Vocabulary Associated with Polynomials Is the given expression a polynomial? Why or why not? 1) 2p2 5p 6 2) 8r3 7r2 4 5 3) c3 5c2 4c1 8 4) 9a5 5) f 3/4 6f 2/3 1 6) 7y 1 3 y Determine whether each is a monomial, a binomial, or a trinomial. 7) 4x 1 binomial 8) 5q2 monomial 9) m2 m 13 10) 11c2 3c binomial trinomial 11) 8 monomial 12) k5 2k3 8k trinomial 13) How do you determine the degree of a polynomial in one variable? It is the same as the degree of the term in the polynomial with the highest degree. 14) Write a third-degree polynomial in one variable. Answers may vary. For each polynomial, identify each term in the polynomial, the coeffi cient and degree of each term, and the degree of the polynomial. 15) 3y4 7y3 2y 8 16) 6a2 2a 11 17) 8n 5 18) 4a3 a2 1 2 a 6 Objective 2: Evaluate Polynomials Evaluate each polynomial when a) r 3 and b) r 1. 19) 2r2 7r 4 a) 1 b) 13 20) 2r3 5r 6 a) 63 b) 13 21) 5r 9 a) 6 b) 14 22) r2 7r 6 a) 36 b) 0 23) r4 4r3 2r2 r 24) 4r2 2r 5 a) 47 b) 7 a) 42 b) 2 25) Bob will make a new gravel road from the highway to his house. The cost of building the road, y (in dollars), includes the cost of the gravel and is given by y 60x 380, where x is the number of hours he rents the equipment needed to complete the job. a) Evaluate the binomial when x 5, and explain what it means in the context of the problem. y 680; if he rents the equipment for 5 hours, the cost of building the road will be $680.00. b) If he keeps the equipment for 9 hours, how much will it cost to build the road? $920.00 c) If it cost $860.00 to build the road, for how long did Bob rent the equipment? 8 hours 26) An object is thrown upward so that its height, y (in feet), x seconds after being thrown is given by y 16x2 48x 64 a) Evaluate the polynomial when x 2, and explain what it means in the context of the problem. y 96; two seconds after the object is thrown, it will be 96 feet above the ground. b) What is the height of the object 3 seconds after it is thrown? 64 ft c) Evaluate the polynomial when x 4, and explain what it means in the context of the problem. y 0; four seconds after the object is thrown, it will hit the ground. Objective 3: Add Polynomials Add like terms. 27) 6z 8z 11z 13z 28) m2 7m2 14m2 6m2 29) 5c2 9c 16c2 c 3c 11c2 7c 30) 4y3 3y5 17y5 6y3 5y5 15y5 2y3 31) x4 7x4 9x3 2x4 2x3 4x4 7x3 32) 2a3 8a2 a2 10a3 9a2 12a3 33) 6.7t2 9.1t6 2.5t2 4.8t6 4.3t6 4.2t2 34) 5 4 w3 3 8 w4 2 3 w4 5 6 w3 7 24 w4 5 12 w3 Add the polynomials. 35) 5n 8 4n 3 9n 5 36) 9d 14 2d 5 11d 19 37) 7a3 11a 2a3 4a 5a3 7a 38) h4 6h2 5h4 3h2 39) 9r2 16r 2 3r2 10r 9 40) m2 3m 8 2m2 7m 1 41) b2 8b 14 3b2 8b 11 42) 8g2 g 5 5g2 6g 5 43) (6m2 5m 10) (4m2 8m 9) 44) (3t4 2t2 11) (t4 t2 7) 4t4 t2 4 45) a2 c4 7 10 c3 3 4 c 2 9 b 10c4 1 5 c3 1 4 c 25 9 a12c4 1 2 c3 c 3b 4h4 3h2 12r2 6r 11 3m2 4m 7 4b2 3 13g2 5g 2m2 3m 19 www.mhhe.com/messersmith SECTION 10.4 Adding and Subtracting Polynomials 795
messersmith_power_prealgebra_1e_ch4_7_10
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