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Worksheet_3_&_4_Solutions

Worksheet_3_&_4_Solutions - J-~ MATH 110 NAME...

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-. ---~ J MATH 110 Worksheet 3 September 29, 2009 NAME S'o/u--bvnS Section _ 1. Understand the connection between factorization and the zeros of polynomials; Find all of the real numbers such that a. x 2 + 3x + 2 = 0 X"2-+'?:.x-+-;( -:::: (;c+I)(X+~) =0 ~ _I ~cl -~ Ct/Ie- ~ ~oS· ) b. x 2 - 3x - 10 = 0 X 2._ 3x- JD::: (X - S;)( X + ::{.) .=- 0 So / 5,- Q./vLJ- -;;(. a~ {L-z ~ . 2. Find a polynomial p of degree 3 such that -1, 2, and 3 are zeros of p and p(O) = 1. f ( X)·-:;: (X 1-1 ) ( .x ~ ~ )( X - 5) - ~
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/ 3. Be able to do algebraic manipulations with polynomials; Z Z Let p(x) = X - 3x + 4, q(x) = 3x 3 - 3, and sex) = X - x - 12 then find the following: a. p + q(x) b. pq(x) c. pjs(x) d. (s(x))Z a) (rt1-)(~):::'- (x 7-_3 A .J-4)r{ 3X>- $) -=- 3 X 3 .,.. X '?.-- Sx. + I /:,) Cri}lx)"~ ()(7.._ >x +-4) (3X~-3) s- q 'LQ' _ 3x -7 X 4- i"2- X '3 - 'Sx ·t 1 :x - I"L c) (p Is )( x) -= X 2 - 3)( .)-- If X "l-_X - 1"2- (1') tl '7t '~'} itv<.- yw .. ihc il. l'..t o?CtJ S " 1... _ / '2. X -LA' -;>(-(2 .... ) +x +-/2 ~ (x 2-_ )(- 12..) 1- X +-1'2.- - »)(' +1 X '2._ )(- /"2 / 'r )(""f2-3x + - ;( 'l-_ 'K-I '2.. 4 ('1-) - / + /fv-2X K 2-,;.. Y' - /1-- ()S?hy .f~ ~VlJ1~ ,x -z.. - I X- J 1-- f X''L- J"t ) 'f - ('/. 2_ 'f: - /2..) o -'2A + i'=- '=- I + iG--2X A ""2- -)1"-) 1.-
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h-h I ~ ~ h 7. f '-'x z '2 - ~ i L- - h X :::. J-,h!tX-Z/+ '1. /- x 1.-1 + X-+ y- X1/- x- V_ <. 7 (,. -z. s.. "L ez..' I}/I - (J()S) (f '2:'- - ~ I
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....... .J MATH 110 Worksheet 4 October 1, 2009 NAME ..z / l.vf;'t"Vl S Section _ 1. Be able to do
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