By Ron (Ron Larson) Larson, Robert P. Hostetler, Bruce H. Edwards
I bought this as a complement to the Onliine algebra classification i am taking. provides a few reliable rules on use of the graphing calculator.
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Additional resources for College Algebra: A Graphing Approach
6x3 Ϫ 4x ϭ 2x͑3x 2͒ Ϫ 2x͑2͒ ϭ 2x͑3x2 Ϫ 2͒ 2x is a common factor. b. 3x 4 ϩ 9x3 ϩ 6x2 ϭ 3x 2͑x2͒ ϩ 3x 2͑3x͒ ϩ 3x2͑2͒ 3x 2 is a common factor. ϭ 3x 2͑x2 ϩ 3x ϩ 2͒ c. ͑x Ϫ 2͒͑2x͒ ϩ ͑x Ϫ 2͒͑3͒ ϭ ͑x Ϫ 2͒͑2x ϩ 3͒ x Ϫ 2 is a common factor. Checkpoint Now try Exercise 73. Factoring Special Polynomial Forms Some polynomials have special forms that arise from the special product forms on page 26. You should learn to recognize these forms so that you can factor such polynomials easily. qxd 28 11/10/03 9:06 AM Page 28 Chapter P Prerequisites Factoring Special Polynomial Forms Factored Form Difference of Two Squares Example u 2 Ϫ v 2 ϭ ͑u ϩ v͒͑u Ϫ v͒ 9x2 Ϫ 4 ϭ ͑3x͒2 Ϫ 22 ϭ ͑3x ϩ 2͒͑3x Ϫ 2͒ Perfect Square Trinomial u 2 ϩ 2uv ϩ v 2 ϭ ͑u ϩ v͒ 2 u 2 Ϫ 2uv ϩ v 2 ϭ ͑u Ϫ v͒ 2 x2 ϩ 6x ϩ 9 ϭ x2 ϩ 2͑x͒͑3͒ ϩ 32 ϭ ͑x ϩ 3͒2 x 2 Ϫ 6x ϩ 9 ϭ x 2 Ϫ 2͑x͒͑3͒ ϩ 32 ϭ ͑x Ϫ 3͒2 Sum or Difference of Two Cubes u 3 ϩ v 3 ϭ ͑u ϩ v͒͑u 2 Ϫ uv ϩ v 2͒ u Ϫ v ϭ ͑u Ϫ v͒͑u ϩ uv ϩ v ͒ 3 3 2 2 x 3 ϩ 8 ϭ x 3 ϩ 23 ϭ ͑x ϩ 2͒͑x2 Ϫ 2x ϩ 4͒ 27x3 Ϫ 1 ϭ ͑3x͒3 Ϫ 13 ϭ ͑3x Ϫ 1͒͑9x2 ϩ 3x ϩ 1͒ One of the easiest special polynomial forms to factor is the difference of two squares.
37 107. 91 1 Synthesis 1 ͑h ϩ 6͒ ϭ 1, h Ϫ6 hϩ6 ͑x ϩ 3͒ Ϫ ͑x ϩ 3͒ ϭ 0 2͑x ϩ 3͒ ϭ 2x ϩ 6 ͑z Ϫ 2͒ ϩ 0 ϭ z Ϫ 2 x ϩ ͑ y ϩ 10͒ ϭ ͑x ϩ y͒ ϩ 10 1 1 7 ͑7 и 12͒ ϭ ͑ 7 и 7͒12 ϭ 1 и 12 ϭ 12 In Exercises 95–104, perform the operations. ) 95. 97. 11 Real Numbers 116. (a) ϪC (b) A Ϫ C Խ Խ ԽԽ ԽԽ 117. Exploration Consider u ϩ v and u ϩ v . (a) Are the values of the expressions always equal? If not, under what conditions are they unequal? (b) If the two expressions are not equal for certain values of u and v, is one of the expressions always greater than the other?
For instance, the polynomial 2x 3 Ϫ 5x 2 ϩ 1 ϭ 2x 3 ϩ ͑Ϫ5͒ x 2 ϩ ͑0͒ x ϩ 1 ᭹ ᭹ ᭹ ᭹ ᭹ ᭹ Write polynomials in standard form. Add, subtract, and multiply polynomials. Use special products to multiply polynomials. Remove common factors from polynomials. Factor special polynomial forms. Factor trinomials as the product of two binomials. Factor by grouping. Why you should learn it Polynomials can be used to model and solve real-life problems. For instance, in Exercise 178 on page 36, a polynomial is used to model the rate of change of a chemical reaction.