I AdvAlgReview WS #2: Unit 3

Divide the following polyn~o~m~ia~ls...!:!u~si~n~~Dill.i~

I. (x" - 3x2- I) ~ •. _ 'if -I-39 ~ S-. 2. (6x'- 16x2 +17~342)+D

)i2tDl<"S X'-l+D\c?-3'i£.t-Llx:-1 3X-d. ~- m.,,1: + \,)( -ic,-X 'I t-O)(3"=-5}l"L - (Q '{ ~-t '-I'i..L

- 8XZ.-t-OV. =t _J ~y-z.+\7x.T 8 V "2. t- Ox +-40 -+ to-x z, +~'J.

9X-(o3'7 -q)(+(oDivide the polynomial using Synthetic Division. Write the answer as the quotient plus the remainderover the divisor.3. (x3 + X + 2 ) -:-( X - 3 )

. Name --~-P=~(\ '=AL_.-- _2/22/13 ~d, _

3 10

D \3 1

Factor the following polynomials COMPLETELY! Include given factor in final answer!!!4. f(x) = x3

- 8x2- 23x + 30; (x - 10)

I

- %' -cR. 2>/D eto

Solve the following polynomials for ALL ZEROS given one factor or zero. Include any giveninformation in final answer!!!! z, I I6. f(x) = x3 - '6X2 + llx - 6 ; f(2) = 0 'f. I\f.. +3 7. f(x) = 2x3 + 3x2 - 1; (x + 1)

~ \ -it -~I - ~ lX-3)[x-i)I -'1 .3 0 ex=- ;,);3,U

8. f(x) = X4 + 5x2- 36 ; f( -2 ) = 0 3-

- RJ \ D S D -3 tp 'x -~,.')( 2. + ~Y-I'8'- ~ y -, ~ 3y Xz..Ly'-:L)T 9(}(-2-)-~ 9 -.l'ff 0 C)(t.-tq)L~-l)

9. f(x) = X4 - 4x3+ 8x2

- 16x + 16 ; (x - 2 ) X"+'l ::l)

c2J 1 -~ :!cj -I ~ J,t [x\ff..X L;~z'! ~~ S' 0 (/+4",)&-<-) C2_~ 3, )-Z ) -).

x7-{Y-?..') + L./lY-~ ') >(\..4= 0 J'X - 4,)(-::. ± 2./') LJ J..

I -I s::) 'J..2. 't- 'I.. - )

L2.'1- -~ + \)

~ -I)-IJ\~

Short Answer:

16. The ordered pair represented by f(-3) = 4 is -----.::..(---:3~J-'-I-~)"l...----17. The ordered pair represented by f(5) = 0 is (_5£.-/ _O_)t::.--_

Ze.r.O ~ 3' -~~." ,""",18. If -5 + 3i is a ~ of f(x), what must also be a factor? - J - I -/ L..fL./ ~

. (X-{-S-3;') -/~\-tr19. Factor and Solve: f(x)=3x4 - 81x. -;---

3-x(x. '3._ ';l--j) =L3x[)( -3)[~L- t-~'C\- q') JX=-D) '/.=-3 -st J 9 - 4ll)(g)

c9.

Find ALLzeros.20. x3 + 3x2

- 25x -75 =f(x)

Y!{X+3') -a,5l '2(+3)

{'j2-d5)C X+3)

C0J-5)v21) f (x) = X 4 + x3 + 2X2 +4x - 8

-~..JJ

\ I ?.. L-( - [s-~ ;t -'8 8>

I -I Lf -4 &I a I..j;

22) Solve using the Quadratic Formula. 10x2 =1-8x

-8 ± J (eLf-LtClbY-I)~o_L +- J2(o

~ - JU

ID)lL i- 8)(~1 ::::a- ~ ±- J lDLt -1{ ±Jrz(o

C2l:) 2 [)

< ~C!~[i~~23) Approximate the real zeros using a calculator. Roundto the nearest hundredth.

g(x) = x3 +X2 -4x+ 1

24) Given: I(x) =. - X 3 T -P- ;J..O'l..

e:If 2 of the zeros are -R and $. how many more zeros does it have?

"-/;t

25) What is the least degree of a function! that has zeros 1, 0, and i ?

,I)D)±'\