By Earl Swokowski, Jeffery A. Cole
The newest variation within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well-liked by teachers and scholars alike: its exposition is apparent, the time-tested workout units characteristic numerous functions, its uncluttered structure is beautiful, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 12E, successfully prepares scholars for extra classes in arithmetic via its very good, time-tested challenge units.
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Additional resources for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition
N factors of a Since the total number of factors of a on the right is m ϩ n, this expression is equal to amϩn; that is, aman ϭ amϩn. We can extend this formula to m Յ 0 or n Յ 0 by using the definitions of the zero exponent and negative exponents. This gives us law 1, stated in the next chart. To prove law 2, we may write, for m and n positive, ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ͑am͒n ϭ am и am и am и и и и и am n factors of am and count the number of times a appears as a factor on the right-hand side. Since am ϭ a и a и a и и и и и a, with a occurring as a factor m times, and since the number of such groups of m factors is n, the total number of factors of a is m и n.
3–6: Replace the symbol ᮀ with either <, >, or ؍to make the resulting statement true. 4 ᮀ (f ) The negative of z is not greater than 3. (g) The quotient of p and q is at most 7. (h) The reciprocal of w is at least 9. (i) The absolute value of x is greater than 7. 8 (a) b is positive. (b) s is nonpositive. (c) w is greater than or equal to Ϫ4. 1 1 (d) c is between 5 and 3 . (e) p is not greater than Ϫ2. (f ) The negative of m is not less than Ϫ2. 1 (g) The quotient of r and s is at least 5 .
For example, properties of the polynomial x 2 Ϫ 9 can be determined by examining the factors x ϩ 3 and x Ϫ 3. As we shall see in Chapter 2, another important use for factoring is in finding solutions of equations. We shall be interested primarily in nontrivial factors of polynomials— that is, factors that contain polynomials of positive degree. However, if the coefficients are restricted to integers, then we usually remove a common integral factor from each term of the polynomial. For example, 4x 2y ϩ 8z 3 ϭ 4͑x 2y ϩ 2z 3͒.