# 2.4 - 2.4 Dividing Polynomials Remainder and Factor...

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Unformatted text preview: 2.4 Dividing Polynomials; Remainder and Factor Theorems Use long division to divide polynomials. Long 'ﬂiviaim ai‘ Wign-nmﬁaig I. arrange m Harms- {af' both {Tina dividand 3.1.1411 the: éiviam‘r in dﬁwamimg anmS {if til-i: vaiiahlo. 2:. ﬂivaiﬂa the. fim term Era. tars: dividaad inky the. final“ term: in the divisor; Wide: {mail Elm firm ﬁrm of tho quotiam. 3.. at tilting; awry tam] Eiitiftﬁ divisa; 3:33? {he fits; Lena E12: gin: aha-national Wing the: wanking product immath Elisa dividend wiih lika 'chimﬁ Eimd up. ail. Saharan? £3153: pméuct from 11%: dividend. 5. Bring dawn. the next warm in {he originai dividend and wrjia i: new in: the mmaindﬂr m 3“:er a now divided-iii (a; was thia ﬂaw axprcgaion as; “rim dividend and foam! this; procasa {mail the .s-‘amaind-er can no wager b3 dividadfihia Wili 0mm what} mi: dag-an {if die rcmaiadar éi'ha high-ﬁg momma. €3.11 variable in. 1.11%: manaimiar) is \$3531- a. tim degree of £131: divimn s s 4 4 2 6 --—"""""'/ D1v1de usmg long d1v1510n. Egg—312’“; I (3 '2, LL51 x _ _‘ ,. , ‘" I} 51X")? 3X 1 )_ ‘ ‘1] ‘ L.\ H 3 éxb+ D XLT—Jrox “Lqu Cmﬂox Aroxiéx Use synthetic division to divide polynomials. 5 _ 4 3 _ 2 _ Div1de usmg synthetic d1v131on. w x391 T><——~ (:5) .C >< Lr+>s?’+?rx2+ 2% + L r} i. --I'- i —<1-' 3 «C3. i —-.,I a *3; 6..“ —%. i ’3 3 “*5 C3. "1.5L R. Li 3 3W +‘8 “(Ht __3>< +3X b X XJH ’5‘ 3 2L X—r—XEL J? Yr} LJ 1 O I O 0 “02 if I I 2 l l 1 l 2 2 2 If) Evaluate a 01 nomial usin the Remainder Theorem. . Qu {xcL CI RemaindJL/i WMVW 1,5” vim FPS LLJ Wk}! !S V! R The ﬂiﬁsimz Alg-ﬂrithm b5 X “C , "Hm/v1 (77¢: me51‘?‘ CL“ if) 7C[C) 1&3"ij sad dis} are paiyammisist with {it 3:} \ﬁ {3; 3314:}; the ﬂags-en: of (If; SE} is 313335 tires] or squat to the degree of ﬁt ash than there: exist assigns 3mijsmmis§s (ﬁx ]- and ﬁ“{3€}! such that fist} m sits} - six) *- sis}- ?iviéud Wain: Quaiiw? Einstein The rerissiriifea; rigs} equals £3 or it, is of degree iess than the. ﬁegret: of d 1: 3: 7;. it til”) ii, We say that dim} iiis'iities Ewen—:13 into fix} and min: dist? ass-LE 43% x} are factors {31‘ f1: 1). If f(x) = 8x4 +6x3 +2):2 + 4x+10 , use synthetic division and the Remainder Theorem to ﬁnd X 41;) r :2 51 l 5%; ‘___, j ’ '__— [37 ' 7 <5 {5 4 q [Of/Civic? WWM 5 ._L?- 9 1,440 “as: WWWQW u b mweww ' r 2 g: Use the Factor Theorem to solve a polynomial equation. Solve the equation 12x3 +x2 agar—1 = 0 given that g is a root. ...
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2.4 - 2.4 Dividing Polynomials Remainder and Factor...

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