A22 APPENDIX Review 40 miles 120 miles 62. The Gibb’s Hill Lighthouse, Southampton, Bermuda, in operation since 1846, stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level.A brochure states that the light itself can be seen on the horizon about 26 miles distant. Verify the accuracy of this information. The brochure further states that ships 40 miles away can see the light and that planes flying at 10,000 feet can see it 120 miles away.Verify the accuracy of these statements.What assumption did the brochure make about the height of the ship? Examples of Monomials Monomial Coefficient Degree x6 2 6 2 − x2 3 − 2 3 3 3 0 Since = ⋅ = ≠ x x 3 3 1 3 , 0 0 − x5 −5 1 Since − =− x x 5 5 1 x4 1 4 Since = ⋅ x x 1 4 4 EXAMPLE 1 We have described algebra as a generalization of arithmetic in which letters are used to represent real numbers. From now on, we shall use the letters at the end of the alphabet, such as x , y , and z , to represent variables and use the letters at the beginning of the alphabet, such as a , b , and c , to represent constants. In the expressions x3 5 + and ax b, + it is understood that x is a variable and that a and b are constants, even though the constants a and b are unspecified.As you will find out, the context usually makes the intended meaning clear. A.3 Polynomials OBJECTIVES 1 Recognize Monomials (p. A22) 2 Recognize Polynomials (p. A23) 3 Know Formulas for Special Products (p. A24) 4 Divide Polynomials Using Long Division (p. A25) 5 Factor Polynomials (p. A27) 6 Complete the Square (p. A29) NOTE The nonnegative integers are the whole numbers 0, 1, 2, 3, . . . . j DEFINITION Monomial A monomial in one variable is the product of a constant and a variable raised to a nonnegative integer power. A monomial is of the form axk where a is a constant, x is a variable, and k 0 ≥ is an integer. The constant a is called the coefficient of the monomial. If a 0, ≠ then k is called the degree of the monomial. 1 Recognize Monomials
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