The polynomial in Example 1c) is 7n6 and has one term. We call 7n6 a monomial. A monomial is a polynomial that consists of one term (mono means one). Some other examples of monomials are k2, 7c5, x, and 1 A binomial is a polynomial that consists of exactly two terms (bi means two). Some examples are p 5, 2m2 13, and 3t4 8t2 A trinomial is a polynomial that consists of exactly three terms (tri means three). Here are some examples: y2 5y 36, 2a4 20a2 16a, and 4w4 15w2 21 In Chapter 2, we saw that expressions have different values depending on the value of the variable(s). The same is true for polynomials. 2 Evaluate Polynomials It may be helpful to construct a term and degree table to help you remember the standard form for writing a polynomial. EXAMPLE 2 In-Class Example 2 Evaluate the trinomial y2 10y 3 when a) y 4 b) y 1 Answer: a) 21 b) 14 Evaluate the trinomial n2 7n 4 when a) n 3 b) n 2 Solution a) Substitute 3 for n in n2 7n 4. Remember to put 3 in parentheses. n2 7n 4 (3)2 7(3) 4 Substitute. 9 21 4 8 Add. b) Substitute 2 for n in n2 7n 4. Put 2 in parentheses. n2 7n 4 (2)2 7(2) 4 Substitute. 4 14 4 22 Add. Remember that evaluate means find the value of the expression for a given value of the variable. You are not solving for a variable. YOU TRY 2 Evaluate t2 9t 6 when a) t 5 b) t 4 Earlier we said that like terms contain the same variables with the same exponents. We add or subtract like terms by adding or subtracting the coeffi cients and leaving the variable(s) and exponent(s) the same. We use the same idea for adding and subtracting polynomials. For example, to add like terms in 5x2 3x 4x2 8x, we add the x2-terms and we add the x-terms like this: 5x2 3x 4x2 8x (5 4)x2 (3 8)x 9x2 11x 792 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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