Definition/Procedure Example 10.5 Multiplying Polynomials When multiplying a monomial and a polynomial, use the distributive property. (p. 797) To multiply two polynomials, multiply each term in the second polynomial by each term in the fi rst polynomial. Then combine like terms. (p. 798) Multiply 5y3(2y2 8y 3). (5y3)(2y2) (5y3)(8y) (5y3)(3) 10y5 40y4 15y3 Multiply. (5p 2)(p2 3p 6) (5p)( p2) (5p)(3p) (5p)(6) (2)( p2) (2)(3p) (2)(6) 5p3 15p2 30p 2p2 6p 12 5p3 13p2 24p 12 10.4 Adding and Subtracting Polynomials A polynomial in x is the sum of a fi nite number of terms of the form axn where n is a whole number and a is a real number. The degree of a term equals the exponent on its variable. The degree of the polynomial equals the highest degree of any nonzero term. (p. 790) To evaluate a polynomial for a value of the variable, substitute the value for the variable and simplify. (p. 792) To add polynomials, add like terms. Polynomials may be added horizontally or vertically. (p. 793) To subtract two polynomials, change the sign of each term in the second polynomial. Then add the polynomials. (p. 793) Identify each term in the polynomial, the coeffi cient and degree of each term, and the degree of the polynomial. 3m4 m3 2m2 m 5 Term Coeff. Degree 3m4 3 4 m3 1 3 2m2 2 2 m 1 1 5 5 0 The degree of the polynomial is 4. Evaluate 2x2 5x 9 when x 3. 2(3)2 5(3) 9 2(9) 15 9 18 15 9 42 Add the polynomials. (4q2 2q 12) (5q2 3q 8) (4q2(5q2)) 12q3q2 11282 q25q 4 Subtract the polynomials. (4t3 7t2 4t 4) (12t3 8t2 3t 9) (4t3 7t2 4t 4) (12t3 8t2 3t 9) 8t3 t2 t 5 Chapter 10: Review Exercises *Additional answers can be found in the Answers to Exercises appendix. (10.1) 1) Write in exponential form. a) 8 8 8 8 8 8 86 b) (7)(7)(7)(7) (7)4 2) Identify the base and the exponent. a) 65 b) (4t)3 c) 4t3 d) 4t3 base: 6; exponent: 5 base: 4t; exponent: 3 base: t; exponent: 3 base: t; exponent: 3 3) Simplify using the rules of exponents. a) 23 22 32 b) a 1 3 2 a b 1 3 b 1 27 c) (73)4 712 d) (k5)6 k30 e) p9 p7 p16 4) Simplify using the rules of exponents. a) (5y)3 125y3 b) (7m4)(2m12) c) a a b 6 a6 b b6 14m16 d) 6(xy)2 6x2y2 e) c5 c2 c10 c17 www.mhhe.com/messersmith CHAPTER 10 Review Exercises 805
messersmith_power_prealgebra_1e_ch4_7_10
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