Exponents and Polynomials - XYZ Custom Plus

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818Chapter 12 Exponents and PolynomialsFill in the missing terms in the numerator, and then use long division to find the quotients. [Example 4]27. __x 3 + 4x + 5x + 1x 2 − x + 528. __x 3 + 4x 2 − 8x + 2x 2 + 2x − 429. x 3 − 1 _x − 1 x 2 + x + 130. x 3 + 1 _x + 1 x 2 − x + 131. x 3 − 8 _x − 2 33. Find the value of each expression when x is 3.a. x 2 + 2x + 419b. x 3 − 8 _x − 2 19c. x 2 − 45x 2 + 2x + 432. x 3 + 27 _x + 3 x 2 − 3x + 934. Find the value of each expression when x is 2.a. x 2 − 3x + 97b. x 3 + 27 _x + 3 7c. x 2 + 936. Find the value of each expression when x is 2.35. Find the value of each expression when x is 4._ 257 _ 5 3 a. x + 37a. x + 13b. _x 2 + 9x + 3 _ 257 b. _x 2 + 1x + 1 _ 5 3 c. x − 3 + _18x + 3 c. x − 1 + 2_x + 1 Applying the Concepts37. Golf The chart shows the lengths of the longest golfcourses used for the U.S. Open. If the length of theWinged Foot course is 7,264 yards, what is the averagelength of each hole on the 18-hole course? Round tothe nearest yard.404 yardsLongest Courses in U.S. Open HistoryTorrey Pines, South Course (2008)Bethpage State Park, Black Course (2009)Winged Foot Golf Course, West Course (2006)Source: http://www.usopen.comOakmont Country Club (2007)Pinehurst, No. 2 Course (2005)7,643 yds7,426 yds7,264 yds7,230 yds7,214 yds1338. Car Thefts The chart shows the U.S. cities with thehighest car theft rates in a year. How many cars werestolen in one month per 100,000 people in Modesto,CA? Round to the nearest car.61 carsU.S. Cities With Highest Car Theft RatesLaredo, TXModesto, CABalersfield, CAStockton, CAFresno, CASource: U.S. Today Snapshot742727685664642per 100,000 in populationNOT FOR SALE. Copyright XYZtextbooks Last re
Chapter 12 SummaryNOT FOR SALE. Copyright XYZtextbooks Last reEXAMPLEs1. a. 2 3 = 2 ⋅ 2 ⋅ 2 = 8b. x 5 ⋅ x 3 = x 5 + 3 = x 8_ xc.5x = x 5 − 3 = x 23d. (3x) 2 = 3 2 ⋅ x 2 = 9x 2e. 2 _3 3 = 23_3 = _ 83 27f. (x 5 ) 3 = x 5⋅3 = x 15g. 3 −2 _= 1 3 = _ 12 92. (5x 2 )(3x 4 ) = 15x 63.12x 9_4x 5 = 3x 44. 768,000 = 7.68 × 10 50.00039 = 3.9 × 10 −45. (3x 2 − 2x + 1) + (2x 2 + 7x − 3)= 5x 2 + 5x − 26. (3x + 5) − (4x − 3)= 3x + 5 − 4x + 3= −x + 87. a. 2a 2 (5a 2 + 3a − 2)= 10a 4 + 6a 3 − 4a 2b. (x + 2)(3x − 1)= 3x 2 − x + 6x − 2= 3x 2 + 5x − 2c. 2x 2 − 3x + 4× 3x − 26x 3 − 9x 2 + 12x+ − 4x 2 + 6x − 86x 3 − 13x 2 + 18x − 8Exponents: Definition and Properties [12.1, 12.2]Integer exponents indicate repeated multiplications.Product Property a r ⋅ a s = a r + s To multiply with the same base,you add exponents.Quotient Property_ a ra = s ar − s To divide with the same base,you subtract exponents.Distributive PropertyExpanded Distributive Property(ab) r = a r ⋅ b r Exponents distribute over multiplication. a _br_= arb rExponents distribute over division.Power Property (a r ) s = a r ∙ s A power of a power is the product of the powers.Negative Exponent Propertya −r = 1 _a rMultiplication of Monomials [12.3]Negative exponents imply reciprocals.To multiply two monomials, multiply coefficients and add exponents.Division of Monomials [12.3]To divide two monomials, divide coefficients and subtract exponents.scientific notation [12.1, 12.2, 12.3]A number is in scientific notation when it is written as the product of a number between1 and 10 and an integer power of 10.Addition of Polynomials [12.4]To add two polynomials, add coefficients of similar terms.subtraction of Polynomials [12.4]To subtract one polynomial from another, add the opposite of the second to the first.Multiplication of Polynomials [12.5]To multiply a polynomial by a monomial, we apply the distributive property. To multiplytwo binomials, we use the FOIL method. In other situations we use the Column method.Each method achieves the same result: To multiply any two polynomials, we multiplyeach term in the first polynomial by each term in the second polynomial.Chapter 12 Summary819
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12.1 Problem Set 759Problem set 12.
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