Section%201.3

Section%201.3 - . 9 96 ICU/c O 8 MA 180 - Precalculus...

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Unformatted text preview: . 9 96 ICU/c O 8 MA 180 - Precalculus Professor Terry Section 1.3: Algebraic Expressions E3 Deﬁanns Asetisa (L0 chilkom. 9 GDQ gem/L6) Rig ,7] Theobiects are called athﬁ €i~e media Q Q ‘i’U €64 Rae MMKW’CQLE \€%u% aibcq.u. E denotes the set of real numbers. Z denotes the set of integers. 3') ‘2 .1 61M 0 CK Two sets S and T are equal (8 = T) if S T CA0. 00% am; 4X (lg/gigg sz—M \$m€ Qfﬁ med E” 64,1" 8 (AMI. T cow: Mo‘i 4.5wa 3.0% FTCLQOJLQ Prsi Algebraic Expressions 35344 xbb ﬂrﬂ « Domain -3( 93} "In/L2 (JEWOJMOGLQQ/ Find the Domain of the algebraic expression: I ‘0 hﬁm Y: Li x \FX—‘4-O‘ X >/O L(2+L{(L{)-—(a ><=io W 2 (ewe-C9 ? <9 A monomial in x is (Lin L1; yakaf‘f‘i'ﬁeam‘ ,9 Q N ' 2 E grow" rm six n \ Abinomialis \(l ﬁnk/M Cg +WO mommioL/(S Atrinomial is \0. 45% O ‘Hvﬂﬂﬂ Wm m \ (XX/5 ' n h-i A polynomial in x is a sum of the form: an x —|— (1m .x _+ ‘ I + QQXQ+ a x + a0 . * ‘ l where n is a nonnegative integer and each coefficient an is a real number. If an :20, then the polynomial is said to have degree H . MA180 Sec1.3 Fail05 ewt . k . Term ch/Q\ LQSLPF‘CSSIUQ Lka in W Cauum i6 tab-twain 0‘; W Leading Coe Icient ‘ R X Examples Leading Coefficient mama—27 “ 7x +10): 8 5 ZSXO By definition, two polynomials are equal if and only if . ‘ P SQ WW Aﬂﬂ‘fm 3 013996 UL“)QL5 9Q like PM “D a Zero polynomial DC We ‘52" ' All Codgtwds cwz 10/0, Constant polynomial _.[ . Nonpolynomials X24 5x + 31? :3 X2,‘ 36‘, _f_ yéﬁm Us " @ 6X3-ax2—tW—5 2 5x3~82x2+ ‘5 t I K @ 'X'HS A ' in 5 Multi i in Pol nomials ( gbwohemk O Q W 'Express asapolynomial: (5x+4y)(5x—4y) z Ftw "Haj: a [5355an m9?- ‘ Express asapolynomial: (5x—4y)2 :2 (‘3 X‘L—(g 3(6Y‘Hj) :’ Q‘SXQ—«ZOK “20 Express as a polynomial: (ﬁ+ﬁ)2(J;—ﬁ)z 2£QT+ ) _. fig >la “@"ﬂﬁﬂmzﬂl 1L MA1BO Sec1.3 FaIIOS ewt 2 l X 2 —— OZZY/(9 "ttj Q Factoring Polynomials Factoring is the process of expressing a sum of terms as a product. lrreducible (or prime) polynomials Greatest common factor (1 if: f) Lt Factor: 5x3+10x2—20x—40 --= 5 (X3 ‘t 2 Y? F” L" X" g) a =-s[x2()§_:a\-Li(x__+§)} g s 5 C)“ =1 lgjjjwfxx ---------- —* 2 T We show see a) *2 50w) (W) M.___._W,ww:;;;_w > m__-.__. ,ﬁ__,,,,e.___...w__ﬁ_ Factor: 7x2+10x—8 "1'- (FTX n 43(X + 2 'chwa 9 T:%M34§” \ t 5 (1' l 0) b—F'C'g) ‘2 5% xiii-filo w r W g; h venom a w-“ .i m -—g Factor: x3—25x i 2XC7J€~H —i aCWx—bl) 3 — 7.- K '&5X 2 X (X 29)” 2 ﬁx—LQOHQ) Factor: 125x3+8 2 (5x33 +6.1); gm 0% 2 W5 [ @143be :: (Q.+b)(6tlwaﬂo+iol) 1;: 5X lo: a MA180 Sec‘i .3 Fall05 ewt i! Sim Iif in Rational Ex ressions Fractional expression i 62., ﬁbuo thew/Q“ I 9C M LQACGV‘K’DEVQWG ' Rational expressions tr, go Cbbuo +1 0 g m P0 RID n E 6? CH0 —5x+4 'Find the Domain of the algebraic expression: , 16 X2.. [ Le :(: O x‘ _. I ' ""' "ﬁgrmii—‘X W xixwamaﬂﬁ' M 'ﬁpiq? 2 2 2 2_ Simplifytheexpression: MAW 2 5W” . Q 20‘ \$14—16 ' 024‘! ammo 23a3+20a+ti .2 C5a+23( (1+2) CLCa—Q) (aziom’amg ‘ (W5 M 23(50sz L/ Mo}; cum Sim Iif the@ 12x _ 3 +2 p y p I 2xl+1 2x2+x x _-.- "3X 3).?— ..... 3‘ + 2; QX‘H H axril x(2x—+D x 3m; Acoaxﬁamb z [axz‘ _. i— + lax+§ Hum "(ZXJ‘B XCZX—H) 2 (Dr? F 5 ~HOH< 22x2+x 2 3431141) W—Zxﬂ) :3 l2x?_ﬂ99_~5i3 ? :2wang 2 Manhpma X (Zoom) I} “a a (2 f)?— Q6463 MA180 Sec1.3 Fall05 ewt + (MW) <w-5Y'Yef A E, VH0 I \ F A CTOR 52/ 3 ' CCaX— 539(y1-H-{3C95 ﬁéx—6)(Qx)+ Q21L0<3X59j CQ)(Q£~5Y(XQ+%[JZ x2~10y + 63);: 5693 [\$2 (Cox—532(X1‘9Lf) 6) E X2 ~lox_{ __ _‘ 7H" 4.__-_,_ ,7 -—.rad——WM“-w___ﬂ_._~_,__k____m%m ...
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This note was uploaded on 04/25/2008 for the course MATH 30191 taught by Professor Terry during the Spring '08 term at Montgomery.

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Section%201.3 - . 9 96 ICU/c O 8 MA 180 - Precalculus...

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