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# Preliminary Objectives- Objective 1 MAC1105

FSU

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This 9 page Class Notes was uploaded by Michaela Maynard on Sunday September 20, 2015. The Class Notes belongs to MAC1105 at Florida State University taught by Pennington LeNoir in Summer 2015. Since its upload, it has received 168 views. For similar materials see College Algebra in Calculus and Pre Calculus at Florida State University.

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Date Created: 09/20/15

852quot 5 MAC 1105 Lecture Outline for Dr LeNoir s lecture classes Our course starts with an algebra review in Objectives 15 A lot of this material should be familiar to you 39Please be careful about judging th adj ffiugglmgfd the entire course based on the rst few dams In Preliminary Objectives 14 we will review the basic factoring techniques that will be used throughout our course Preliminary Objective 1 Factoring out the Greatest Common Factor GCF in a polynomial of one variable Note For the variable terms the eb b exponent is the MOQL that s common 48m5 8x3 4132 Laws of Exponents 3 ha m M LIX lax not l am anzom ab Ow b m h a m on a m 2 1 aquot O b b L amnij aim a M Our main emphasis will be factoring out the GOP when there is a negative coef cient on the highest power of 2 As we use this technique in Obj 1 and 3 It will be your choice whether or not to factor out the minus sign in your initial factoring step 52x3 13x4 52x3 1302 Ll gt 13 3 x quot3 0 39 4 Xi H gt 3x3xquot4gt 2235 55a6 22x5 556 MPG 5x my a t Sk H355 5k 2 Preliminary Objective 2 Factoring the Difference of Two Squares mtgEQW quot sum 0 square I 25332 9 25x29 Does n21 fatter 5x 3 5 r 3 Our main emphasis will be factoring the difference of two squares when there is a negative coe icient on the variable term i 25 35 3 g 9 i I 4 amp 3 5L 3 1 432 1 quot39 4132 1 300 Vat quot gvan amt 1 Preliminary Objective 4 The relationship between a b and b a 391 a 1lta bgt 0 rb 1b a 9 boa Q b Conclusion They are n or 2E2 of each other 5 8 33 1 3 22 139 O quot a Slmp lfy 5 8 1 c I 293 3 l Note ab 5 M A Same Preliminary Objective 3 Factoring Quadratic Trinomials Note Many of the problems in our course contain a hint for the trinomial factoring Use It Before we factor recall how to multiply two binomials F O I L Multiply das 52v3 c 5 x ug2xbz33951l 6 mg m We M5 m mm 40 3943 my agx M5 Rx nds We ll use Reverse F O I L in order to factor For some problems one factor will be known you will need to determine the other For some problems you have to be able to factor with no hint Two eGrade examples Complete the factoring 18x2 191 12 21 3ax J b Enter a and b as an ordered pair however if the operator is subtraction then you must enter b as a negative number For example 95123 3 you would enter 2 3 for 21 3Lvoujvould ente rQ3 r 18x2 19x 12ax 3gtQy 4 39Vq Ll th hKc Complete the factoring 1812 331 14 61 7ax l b See eGrade instructions above 18m2 33x14p 7gt3 2 Factor 18x2 51m8 24132 753 5 4A l2c 3 723937 5 4K 5 9x 15 1 qt MOO 54 q x 6l 3quot 5100 It W 1 3x 4 quotfa 8x 5 3x xlYX l39Y 39 quotX39a 3 blab lobx a q JimMg 014 395 These problem are in MultiFormula mode enter factors separated by semicolon lulut iWMh QaUchm I 3quot X 2 39 rst equals a 0 m La t equals a b rm Objective 1 Rational Expressions fractions made up of Ol 3 Note Values that cause division by zero are called r oryn th variable We ll do more with this concept when we study function domains in Obj 100 We will not list restrictions on the vbl as we work in Obj 1 b f O Obj 1a Recognizing Equivalent Rational Expressions In particular dealing with a pesky minus sign when it appears in front of a fraction Consider a numerical fraction 4 3 3 35 We will ask Which are equivalent to the given expression and the problems will be in Multiple Selection mode You will choose all that are equivalent if none are then select that choice Plan of Attack Generate equivalent expressions by distributing the minus through the M then separately through the Q Q Compare these with the answer choices Or you may nd that you can simply compare each choice with the given expression Keep in mind Prelim Obj 4 a b b a Which are equivalent to 33 6 X39U xLp Vb 12 X 2 L1 X U xo U39N c 1 x 1 a6 6 c Answer choices None are equivalent Which are equivalent 0 32 39 jg 4i 3 2 x z X l z X 41 2 b quotz gt Z Z gt m xz Answer choi es x z None are equivalent CL 9 4 b 0 d Objective 1b Multiply Divide Rational Expressions 9 Q 1 lo C Plan of Attack Factor Ever thi Three types of factoring Factor a trinomial ways factor it Ia b Use the hints provided by the other factors Remove the GCF Factor the Difference of Two Perfect Squares x2 y2 When cancelling common factors remember Prelim Obj 1 2 1 2x2 5x 12 M F i x 5 Simplify 29525 m a 39 quot39gt 42 20 3 MC 33fcx 5 9 20939s x W 6x3 lain 3gt an 6 2012 23cc 6 101 Slmpllfy39 9 1632 39 4m2 10x3 I I 5 5 MM W W6 uquot x qua O O 25 Ex4 g2 an 535 QL 9 f559Q S mphfy39 2x2 1313 20 36 A r 5 4 6 2 F Q 5W rat39s Mam on WM can O I DKJ5 01Lgtgt BOILl laba T 3 F 3 21L 0c abs 9115 Objective 1c Add Subtract Rational Expressions Plan of Attack Use the Least Common Multiple to create a common denominator in each fraction Determine the LCM For terms containing the variable use the highest power in any one denomi nator 90 Ob fed Cb GOLUDV nam Era r Create the common denom in each by comparing each fraction s denom with the LCM and them by multiplying each fraction topandbottom by the part missing from the LCM 2 1LCM 29 5 7 CMZ 1h Sunphfy392 6 3 8 582 Slmpllfy 62 6Z5 E a Loa fxa 3L 3amp J5L Zg I 23912 at 9x quot 8k 3 3 5b 4 a W 49x 30x 3 67 w x3 3quot 3 3amp3 if a 3 81 quot 20L 3 Once W 5 H quot 722 Simpl i39 1Z152 5quot Wm one 3 F9 3 L 5 3x 31 qxq11 at 3L3 k j 3 51L 39 3o cqrc lgucg 3 3 9 3mquot 3wquot wabch lyncj e a common Simplify 8 19 X W Y m ma 3 how 5132413 12 2x25x 42 qa 0me 8 Hui q n a mac wgt 57W Samoa lt5 m BCK39LQ a 5 394 BX a 3 439 zaampb7 Cit3 k bax7 nRCCpampu7 3 EWWY mum on o n e 19 7 e wade a wv S mphfy 3x2 11x 20 a23c 10 44604 763w lq d 23 BMW Twila5 W WOW 14x3x 2u 23 5 1 VOL quot W 1quot mittMb Hmt39 inbmml 3 f 0 actor 0 mole an Simplify 4923 3 1 490 5 Simplify 33323 g 1 6 3336 qHSSCK g 3g 5 f 3 Q 3Kq 393 6b 3amp gtL 0 Caliquot at f 39 9 5za was toe 3 3 5 3x123 773 31 Mwbm39f w gy 5 32 004 0 3quot 3x 41 Big La 4 pg 104 33x ll 5 KM 41c 5Kagt 45 5L39gt aw M C a Wan 52 iwr 128 i229 39 41SXLaz gr on ID 33 o quot m Simplify 5x28529116 6352 Simplify 6332131136610 5 3 29 5 KW C gt 134quot g 1 31 lq 3 quotH39 x2lt2x5gt 572x 5mm 9 5 0 quot 5 A 3 N UUatCln neg 35573 763Li3928 by 44516 y 5 37 3uA Art 0255 3mm J r SKI a Lo 46W A Can not 19C f 3L Li 363KAgt T actored7redu39ct 23 Further 3quot Rgt 3V5 drawer 5b 37 3 6 4 39 4 4 U 139 qt 0 Objective 1d Simplify mixed quotients complex fractions There are two common methods used for Simplifying mixed quotients I ll demonstrate the method that I think is best both methods are Shown on the Video clips for this objective 8 n L a 6 Plan of Attack Determine the LCM of all fractions n n U m Olen the h Multiply top and bottom of the blg fractlon by the LCM of all A we t MAI b 3 3 3 d c d 39c 739 d a 9 C Smphfy 3 3c 3 c 3c 3s g ac 3d d c c c c CCQ C Cd c 3 Cd39C2 36 9 3C 0 8 1 LDC 39 36 LOC 36 Jinn d 9c 6 A Mull Chowe 1 fadLCMi 33 1 0 eh L w gt 39439 39 231 I 39 Simplify Elf l V own 3 2 g qw wy H J m3 a i w 5 W quot39 W J39MUH thence wr j s 1w 1a i r 4 4 u lmpl a w a66 TE a m quot quot am a Mb 9 am a Ma a Ma a 9 0 M T 1 FA Simplify 54 2 X rW XL 1 C4 Li L V A XH l m M 111 3 N x H 1 9 W z M YB f3 1 L Sunplify 1 A 39T 39 GTE 5 77 LL31 5 fs 9 4 tj 7 4 o 39gr a q Simplify Beduce completely to a simnle fraction Enter the answer as an ordered pair a b If negative you must enter the minus Sign with a For example 1 3 71 you must enter 13 For integer answers you must enter b as 1 For example 3 55 you must enter 31 3 51 quot5 2 0 Simplify Simplify 4 7 1 3 I 1 2 T I 3 t 5 2 C3 quot39 0 3 73957 31 5 70 0 2 7 7 1 ab a C0 3 39 0 vi 139a 5quot e 30 Y w a JKExMCY C J 5 1l7llcgt39lquotaio 3939 1 5 3 1 1 g 3 p v 2c a Simplify 932 5 Simplify 32 5 3 1 r at 1 lt gt i 5 l 5 3 l r L I quot R 3 5 q aj q 3 75 3 27quot 3 5 5 5 01 KM 5 5 28 9 3 3 539 39 7 3 72 1 I l ak Emen W rEYibfY 356 gal 5 3n 23 Ce Simplify 1 15 4 q 4 Simplify 3 2 a g were 1e if 0 3 a i 13 T 92 3 q 3 q 1 33 69 4 739 3 25 18 L a T L 3 Eheew p w 5 l I I l 7 9r F 3 Ira quotl Uge Mugabe mam a 5 Write in sim lest radical form SRationalize the denominator simplify and reduce completely Enter tmrmn answer negative the minus Sign must be entered with the numerator For example 35 The answer must be entered as 3sqrt25 or as 3sqrt2 5 Vii 035 gig FL wo i 1 5 fr g 43 5 F5quot EE L 4 W rTE rl 4 5quot 51 our r 39 AtaKe w ate4045 4 M c 535 B BsqrtC V Li H g 3 373 qi gz J MWEQ 3 61 3 5 x 5 D 3 3f 3 V 5 clt 5535 5 4 l lm 6 0 quot39quotquotquot I fTg TEESquot 396 quot 3 alumsB 3 WE VE 239 wi Ifquot 4 a quotU qu bc3 E 1 15F5 JE ljlg 6 1 1 5 o a 5 5 SELL 4 I3 614 E H r54 F 5quot 95 543 3 059 22 47 936 F V5 5gt6l5 2 f L 2 sanser 35qlta 3

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