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# Algebra I Chapter 8

Algebra I Chapter 8

GET READY for Chapter 8Diagnose Readiness You have two options for checking Prerequisite Skills.Option 1Option 2Take the Quick Check below. Refer to the Quick Review for help.Take the Online Readiness Quiz at ca.algebra1.com.Rewrite each expression using theDistributive Property. Then simplify.(Lesson 1-5)1. 3(4 - x)2. a(a + 5)3. -7( n 2 - 3n + 1)4. 6y(-3y - 5y - 5y 2 + y 3 )5. JOBS In a typical week, Mr. Jacksonaverages 4 hours using e-mail, 10 hoursof meeting in person, and 20 hours onthe telephone. Write an expression thatcould be used to determine how manyhours he will spend on these activitiesover the next month.Find each product. (Lesson 7-6)6. (x + 4)(x + 7)7. (3n - 4)(n + 5)8. (6a - 2b)(9a + b)9. (-x - 8y)(2x - 12y)10. TABLE TENNIS The dimensions of ahomemade table tennis table arerepresented by a width of 2x + 3 and alength of x + 1. Find an expression forthe area of the table tennis table.Find each product. (Lesson 7-7)11. (y + 9) 212. (3a - 2) 213. (3m + 5n ) 214. (6r - 7s ) 2EXAMPLE 1Rewrite n (n - 3n 2 + 2 + 4_n ) using theDistributive Property. Then simplify.n (n - 3n 2 + 2 + _ 4 n ) Original expression= (n)(n) + (n)(-3 n 2 ) + (n)(2) + (n)(_4 n )Distribute n to each term inside the parentheses.= n 2 - 3 n 3 + 2n + 4 Multiply.= -3n 3 + n 2 + 2n + 4 Rewrite in descendingorder with respect to theexponents.EXAMPLE 2Find (x + 2)(3x - 1).(x + 2)(3x - 1) Original expression= (x)(3x) + (x)(-1) + (2)(3x) + (2)(-1) FOILMethod= 3x 2 - x + 6x - 2 Multiply.= 3x 2 + 5x - 2 Combine like terms.EXAMPLE 3Find (3 - g ) 2 .(3 - g ) 2 = (3 - g)(3 - g) Laws of Exponents= 3 2 - 3g - 3g + g 2 Multiply.= 3 2 - 6g + g 2 Combine like terms.= 9 - 6g + g 2 Simplify.Chapter 8 Get Ready For Chapter 8 419

8-1 Monomialsand FactoringMain Ideas• Find primefactorizations ofmonomials.• Find the greatestcommon factors ofmonomials.Preparation forStandard 11.0Students apply basicfactoring techniques tosecond- and simple thirddegreepolynomials. Thesetechniques include finding acommon factor for all termsin a polynomial, recognizingthe difference of twosquares, and recognizingperfect squares of binomials.New Vocabularyprime numbercomposite numberprime factorizationfactored formgreatest common factor(GCF)In the search for extraterrestrial life,scientists listen to radio signals comingfrom faraway galaxies. How can theybe sure that a particular radio signalwas deliberately sent by intelligentbeings instead of coming from somenatural phenomenon? What if thatsignal began with a series of beeps in apattern composed of the first 30 primenumbers (“beep-beep,” “beep-beepbeep,”and so on)?Prime Factorization Numbers that are multiplied are factors of theresulting product. Numbers that have whole number factors can berepresented geometrically. Consider all of the possible rectangles withwhole number dimensions that have areas of 18 square units.1 182 9 3 6The number 18 has six factors: 1, 2, 3, 6, 9, and 18.Prime and Composite NumbersWordsExamplesPrime NumbersBefore deciding thata number is prime,try dividing it by allof the prime numbersthat are less thanthe square root ofthat number.A whole number, greater than 1, for which the onlyfactors are 1 and itself, is called a prime number.A whole number, greater than 1, that has morethan two factors is called a composite number.0 and 1 are neither prime nor composite.2, 3, 5, 7, 11, 13,17, 194, 6, 8, 9, 10, 12,14, 15A whole number expressed as the product of prime factors is called theprime factorization of the number. Two methods of factoring 90 are shown.Method 1 Find the least prime factors.90 = 2 · 45 The least prime factor of 90 is 2.= 2 · 3 · 15 The least prime factor of 45 is 3.= 2 · 3 · 3 · 5 The least prime factor of 15 is 3.420 Chapter 8 Factoring

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