Addition & Subtraction of Polynomials

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Transcription:

Addiion & Sucion of Polynomil Addiion of Polynomil: Adding wo o moe olynomil i imly me of dding like em. The following ocedue hould e ued o dd olynomil 1. Remove enhee if hee e enhee. Add imil em. Wie nwe in decending ode wheneve oile Emle: Add nd. Soluion: Since hee e no ny enhee, dd he imil em nd wie he nwe in decending ode. Emle: Add. Soluion: Remove he enhee, dd he imil em nd wie he nwe in decending ode. Emle: Add. Soluion: Remove he enhee, dd he imil em nd wie he nwe in decending ode. 1 Emle: Add 1. Soluion: Remove he enhee nd dd he imil em. Since hee e wo vile, don woy ou decending ode. 1 1 1 1

Sucion of Polynomil: Sucing wo o moe olynomil i lo me of comining like em; howeve we mu e ceful when emoving he enhee ecue he negive ign in fon of he enhee mu fi e diiued mong ech em in he enhee heey chnging ll he ign. In eence we e uing he diiuive oey o mulily negive one hough he enhee. 1. Remove enhee nd chnge oie ign vlue.. Suc imil em. Wie nwe in decending ode wheneve oile Emle: Remove he enhee nd imlify 1. Soluion: The fi e i o emove he enhee. When emoving he enhee fom he nd olynomil e ue o diiue he negive ign -1 hough evey em. 1 1 1 Emle: Remove he enhee nd imlify. Soluion: The fi e i o emove he enhee. When emoving he enhee fom he nd olynomil e ue o diiue he negive ign -1 hough evey em. 1 Emle: Suc fom. Soluion: Be ceful of he woding on hi olem. Becue we e ucing he fi olynomil FROM he econd olynomil, we mu wie hi follow: Now h i i wien coecly, imlify uul.

Addiion & Sucion Togehe: Thee emle will conin oh ddiion nd ucion. The ocedue i he me in eviou emle. To comine men o eihe dd o uc oie. Emle: Comine. Soluion: I m going o ki ome e which y now we hould e le o do menlly. 11 Emle: Comine. Soluion: Emle: Comine. Soluion: 1 Emle: Simlify. Soluion: Noice he negive in fon of he fi olynomil. Emle: Simlify 1 1 1 1 1. Soluion: 1 1 1 1 1 1 1 1 1 1

Alicion: Emle: The ol U.S. imo of eoleum in million of el e dy in given ye i oimed y he olynomil 0 00 0, whee eeen he nume of ye ince. The coeonding nume of eo of eoleum i given y he olynomil 0. Wie olynomil h eeen how mny moe el e dy wee imoed hn eoed in given ye. How mny moe el e dy wee imoed in he ye 1? Soluion: To find olynomil h eeen how mny moe el e dy wee imoed hn eoed in given ye we mu uc he wo olynomil. 0 0 00 0 00 0 0 0 0 0 To deemine how mny moe el e dy wee imoed in he ye 1 we mu evlue hi olynomil fo he vlue =. 0 0 0 0 0 0 0 Aoimely,,000,000 moe el e dy e imoed hn eoed. Emle: The ol eene in illion of doll in fedel U.S. hoil cn e modeled y he olynomil 0. 1, whee i he nume of ye ince 1. Fo non-fedel U.S. hoil, he coeonding olynomil i1. Wie olynomil h eeen he ol eene fo ll U.S. hoil. Wh wee he ol eene in 1? Soluion: To find olynomil h eeen he ol eene fo ll U.S. hoil we mu dd he wo olynomil. 0. 1 1 1. To deemine he ol eene in 1 we mu evlue he olynomil =. 1. The ol eene in 1 wee $1 illion. 1. 1 1

Emle: The nume in million of DVD old in given ye i oimed y 1 00, whee eeen he nume of ye ince 1. The nume of video e in million old duing he me ime eiod i 0 1 0. Find he olynomil h eeen how mny moe DVD hn video e wee old in given ye. How mny moe DVD hn video e wee old in 00? Soluion: To find he olynomil h eeen how mny moe DVD hn video e wee old in given ye we mu uc he olynomil. 1 00 1 00 1 0 0 0 1 0 1 0 To deemine how mny moe DVD hn video e wee old in 00 we mu evlue he olynomil = 1. 1 11 0 0 0 1 0 1 11 0 Thee wee,0,000,000 moe DVD hn video e old in 00.

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