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# Class Note for MATH 1300 with Professor Flagg at UH

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Date Created: 02/06/15

Math 1300 Solving Equations by Factoring Definition The zeroproduct pro a0orb0orboth Definition A quadratic equation where a b and c are numbers an Solving Quadratic Equations To solve a quadratic equation we 0 0 Factoring is usually a help move all nonzero terms to one sir use the zeroproduct property Examples 1 Solve the equation x2 7 5x 7 Only the lefthand side LHE of terms is necessary Facto Factor ZPP x Solve for x 2 Solve 2x218x772 0for All nonzero terms are on the Factor 2 ZPP x Solve for x J 3 Solve the equation 6x2 7 27x This equation has nonzero tlt possible to solve move the 7 6 Factor 31 ZPP 2x 7 Solve for x 4 Solve 16x2 71 Subtract 1 from both sides 16x2 7 1 0 Factor ZPP 4x710 or 4x10 Solve for x x 4 or x quot4 1 5mm 7 0 k x3 O x7gt0 168 PM quotGad a aw 4 1 Ha 12 4 R D lx 3 QXL TyHb 0 4x 7 14x 1 0 Note This is a special polynomial Math 1300 Section 44 Notes 5 Solve 712x2 7 717x 6 This quadratic equation has nonzero terms on both sides of the equal sign so we must move all the terms to one side Add 17x 7 6 to both sides and solve 7122 17x 7 6 7 0 Factor 71 4x 7 33x 7 2 0 Note 71 0 ZPP 4x730 or 3x720 Solve forx x 34 or x 2 6 Solve for x xx 7 2 71 Make one side equal zero xx 7 2 l 0 Distribute x2 7 2x 1 7 0 Factor x 7 l2 0 Note This is a special polynomial ZPP x71 0 Note Noneedtowntex710tvvice Solve for x x 1 Solving Other Polynomial Equations Solving other polynomial equations is done just like the quadratic equations Set one side of the equation to zero factor use the zeroproduct property and solve for x Facior GCF M X Examples 1 Solve4x316x215x0 XLfXL E 6X l9 0 This polynomial is already equal to zero so all we need do is factor use the ZPP and solve for X 4x316x215x 0 Factor x2x 52x 3 0 ZPP x0 or 2x50 or 2x30 Solve for x x 0 or x 3952 or x 3932 2 Solve x3 2x2 99x Get LHS equal to zero x372x2793 0 Factor xx 7 llx 9 0 ZPP x0orx7ll0orx90 Solveforx x0 orxll or x79 3 Solve 7x3 714x2 7 0 Set one side equal to zero Already done Factor 7x2x 7 2 0 ZPP 7x20orx720 Solve forx x 0 or x 2 Math 1300 Section 44 Notes 4 Solve x3 18 2x2 9x by factoring Set one side equal to zero x3 18 7 2x2 7 9x 0 Rewrite x372x279xl80 Factor x2 7 9x 7 2 0 x3x73x720 ZPP x30orx730orx720 Solveforx x73 or x3 or x2 5 Solve 30x3 7 3x2 7 9x 7 0 Set one side equal to zero Already done Factor 3x5x 7 32x l 0 ZPP 3x0 or 5x730 or 2xl0 Solveforx x0 or x35 or xquot2 6 Solve 2x 712 7 2xx2 7 20 8x2 2 Set one side equal to zero 2x 7 l2 7 2xx2 7 20 7 82c2 2 0 Simplify 2x2 7 2x 1 7 2xx2 7 20 7 8x2 2 7 o 2x274x272x340x78x2720 Rewrite 72x3 7 6x2 36x 7 0 Factor 72xx 6x 7 3 0 ZPP 72x0orx60orx730 Solveforx x0orx orx3 yl gdc ms and 429414 5474 2 cm out CF SW 3 Fm fem 7 poLLMDWH39a 55 4 zero39ProM 51745 5olVe Solve the following equations by factoring 1 3x2 7 5x 2 7 0 Man JUN 54 2 gCF39Vl 74 m Qgtltf DUO Q Fw a73c1 76 b 39 meorboarx I UCoD ero MUM1 14 W b 4 0 Pmtim 3x2l33x73 7173z S 3X 13CX B 2370 370 3x72yx7bo MW Bxlto tn XquotiO 3 Stth 1 3xL Math 1300 2 xjix X giro d 3 x4lt U 4 313 8 3x Pmij fut 5 823 4 gxl Ftux 399 U 39 39 8 5 ac r7 539 2Llgtlt59 9 70 84 1 521 55 3x amxb PW ax 3M47ltW 0 Mathl300 Zero x 4 3 0 LEVl OSection44Notes 1 1 Fl as a 6 3x22x8 Lf Jx lx d 3 11x 3 r 0 PW m3 c 3 aci l b I 1 34 L6 gtlt 9 Pre PM 3x 0 1X Q 3 3 W 3x Lth JD0 era 3x 0 m x lco 1 1f 1 41 7 7 2 x z 7 4M14amp 96 0 3 3 n 90 1x 33 Q 49 x3 42gtlt1 Llt X mix 39 2x Jr 2gtlt 9gtlt2x74lt Lf gt Qx3x 4 337x4 Cpgt c 4 g7 IYK S x Z GFD ampXO 3x 931 7X 13 5 Ci I Q 3 9 7 P e X 0 P J 8 ssx 32x2 L fo 39 Z 7 TC 31 31 X 7 06 3axL O so 9X 2 XL 9 Xxlgtlt CgtltSD 0 X 0 Math 1300 Section 44 Notes 9 4x2 40 44 My dmw HlLWX 0 i O 4xz HX lo 0 5 O K gN DI Lng 0 u n0 0 0 l Y IO L gtlt Dgtlt lo3 t 0 I gtlt U 0 10 wait 1 3 91 U 4 Ca 6 CF X X o 3 7x 397 7gtH g 7 W X 3167 x147 7 x 37 x2 I I 011602627x720 T 7 X 33 x Dlt 0 V 439 l0 X 0 ao c x 20 Y 3 x 4 Mam cg Zng 9 0 arqzwaw ag 25210 1207x2 728 ozxivs 670 Aw ds 745 m 7 1C6x 441 7x1 Q gx GCP 7X 17x x 49 33 X 1 H at W m 6

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