By Ron Larson, Robert P. Hostetler

This market-leading textual content maintains to supply scholars and teachers with sound, continually based reasons of the mathematical suggestions. Designed for a two-term direction, the hot 7th version keeps the beneficial properties that experience made Algebra and Trigonometry a whole answer for either scholars and teachers: attention-grabbing purposes, state-of-the-art layout, and cutting edge know-how mixed with an abundance of conscientiously written routines.

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**Example text**

Explain or give an example. 50 25 x 20 30 40 50 60 Speed (in miles per hour) GEOMETRY In Exercises 117 and 118, use the area model to write two different expressions for the area. Then equate the two expressions and name the algebraic property that is illustrated. x 117. 4 x 1 x+4 x 118. a x a x+a 125. THINK ABOUT IT Must the sum of two seconddegree polynomials be a second-degree polynomial? If not, give an example. 126. THINK ABOUT IT When the polynomial Ϫx 3 ϩ3x2 ϩ 2x Ϫ 1 is subtracted from an unknown polynomial, the difference is 5x 2 ϩ 8.

Simply add or subtract the like terms (terms having the same variables to the same powers) by adding their coefficients. For instance, Ϫ3xy 2 and 5xy 2 are like terms and their sum is Ϫ3xy 2 ϩ 5xy 2 ϭ ͑Ϫ3 ϩ 5͒ xy 2 ϭ 2xy 2. WARNING / CAUTION When an expression inside parentheses is preceded by a negative sign, remember to distribute the negative sign to each term inside the parentheses, as shown. Ϫ ͑x 2 Ϫ x ϩ 3͒ ϭ Ϫx 2 ϩ x Ϫ 3 Example 2 Sums and Differences of Polynomials a. ͑5x 3 Ϫ 7x 2 Ϫ 3͒ ϩ ͑x 3 ϩ 2x 2 Ϫ x ϩ 8͒ ϭ ͑5x 3 ϩ x 3͒ ϩ ͑Ϫ7x2 ϩ 2x2͒ Ϫ x ϩ ͑Ϫ3 ϩ 8͒ Group like terms.

CAPSTONE A third-degree polynomial and a fourth-degree polynomial are added. (a) Can the sum be a fourth-degree polynomial? Explain or give an example. (b) Can the sum be a second-degree polynomial? Explain or give an example. (c) Can the sum be a seventh-degree polynomial? Explain or give an example. 50 25 x 20 30 40 50 60 Speed (in miles per hour) GEOMETRY In Exercises 117 and 118, use the area model to write two different expressions for the area. Then equate the two expressions and name the algebraic property that is illustrated.