By Ron (Ron Larson) Larson, Robert P. Hostetler, Bruce H. Edwards
I bought this as a complement to the Onliine algebra type i am taking. offers a few strong principles on use of the graphing calculator.
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Extra info for College Algebra: A Graphing Approach
3x ϩ 4 xϪ3 Solution 2 x͑3x ϩ 4͒ Ϫ 2͑x Ϫ 3͒ x Ϫ ϭ x Ϫ 3 3x ϩ 4 ͑x Ϫ 3͒͑3x ϩ 4͒ ϭ ϭ ϩ 4x Ϫ 2x ϩ 6 ͑x Ϫ 3͒͑3x ϩ 4͒ 3x 2 3x 2 ϩ 2x ϩ 6 ͑x Ϫ 3͒͑3x ϩ 4͒ Checkpoint Now try Exercise 45. STUDY TIP Basic definition Distributive Property Combine like terms. When subtracting rational expressions, remember to distribute the negative sign to all the terms in the quantity that is being subtracted. qxd 40 11/10/03 9:07 AM Page 40 Chapter P Prerequisites For three or more fractions, or for fractions with a repeated factor in the denominators, the LCD method works well.
4. 5. 6. (b) 1 ؊ 4x3 (d) 7 3 (f) 4 x 4 ؉ x2 ؉ 14 A polynomial of degree zero A trinomial of degree five A binomial with leading coefficient Ϫ4 A monomial of positive degree A trinomial with leading coefficient 34 A third-degree polynomial with leading coefficient 1 6x x3 ؉ 2x2 ؊ 4x ؉ 1 ؊3x5 ؉ 2x3 ؉ x In Exercises 7–10, write a polynomial that fits the description. ) 7. A third-degree polynomial with leading coefficient Ϫ2 8. A fifth-degree polynomial with leading coefficient 8 9. A fourth-degree polynomial with a negative leading coefficient 10.
6x 3 Ϫ 5x 2 Ϫ x ϩ 5 Combine like terms. Ϫ x2 Ϫ 4x ϩ 2͒ Ϫ ͑ 3x 4 Ϫ 4x2 ϩ 3x͒ ϭ 7x 4 Ϫ x2 Ϫ 4x ϩ 2 Ϫ 3x 4 ϩ 4x2 Ϫ 3x Distributive Property ϭ͑ Group like terms. 7x 4 Ϫ ͒ϩ͑ 3x 4 Ϫx2 ϩ ͒ ϩ ͑Ϫ4x Ϫ 3x͒ ϩ 2 4x2 ϭ 4x 4 ϩ 3x2 Ϫ 7x ϩ 2 Combine like terms. Checkpoint Now try Exercise 23. To find the product of two polynomials, use the left and right Distributive Properties. Example 3 Multiplying Polynomials: The FOIL Method ͑3x Ϫ 2͒͑5x ϩ 7͒ ϭ 3x͑5x ϩ 7͒ Ϫ 2͑5x ϩ 7͒ ϭ ͑3x͒͑5x͒ ϩ ͑3x͒͑7͒ Ϫ ͑2͒͑5x͒ Ϫ ͑2͒͑7͒ ϭ 15x 2 ϩ 21x Ϫ 10x Ϫ 14 Product of First terms Product of Product of Outer terms Inner terms Product of Last terms ϭ 15x 2 ϩ 11x Ϫ 14 Note that when using the FOIL Method (which can only be used to multiply two binomials), the outer (O) and inner (I) terms are like terms and can be combined into one term.