Algebra 2

Unit 6 Review

FFind each product.J m

1) (8a — 6)(—7a — S)

5x02314033 +HZa+ ’50

~5xoa" + 23 + ’50

82x ‘ (S

3) (m6)w

)6” 456990): ~L12K2+35K 4‘12

30K.” — \MKZ HQSK ~Liz] -5m

((33

Divide using any method you prefer.

5) (k4 + 2k3 — 77k2 — 29k+ 40) + (k — s) - 6) (3x2 + 24x) + (x + s)

x+8l3x7 +2-Hx- 2'1!

0

~2'1r Ho

7) (v‘+5v3 —4v-20)+(v+5) 8) ("4'2"3 —28n2—14n+8)—:-(n+4)

mn“ ~2n ~2an“-Hn +5

— nq ~ ‘10”

“\pn‘a -28n29 2

Hm +2‘in

- Hn'z‘i‘in

.1. .Lan'J—nnn

Factor each. One factor has been given.

9) f(x)=x3—5x2+8x—4; x—2

X3*5XZ+8X~Ll _ 2

_ ~x+

X-Z x 3 ’2.

’2

X —|)<-Z><+2

(x—OCx—z)

-F(x) = 6&lele

11) f(x)=x3-3x2~25x+75;x—5

3 Z

X " ‘5

X2 HEX -3x -lS(Haw-3) .

~F(x) = (x+6Xx—3Ix—9)

Factor each polynomial completely.

13) n2—11n+30

DZ ~5h-Kon + ’50

(Kn—‘5) -Lo(n“o>

IS) x2+x

10) f(x)=x5+5x4—9x3—45x2; x+3

6 ‘l B 2 3 1 _“X “Ix “W = X"+2x ~st G»

2<+3

x2(x2+2>< — 16>X1(x-3Xx+<5)

12) f(x)=x3 —l9x+30;x—3

: x1+ Bx ~10

X- E)

x1+5>< ~10

(x +5Xx —2)

14) 61? + 6a2

16) x1-.9x+18

x1~3>< 1— la

x(x—3)-\a(x—3)

17) 5112-2717— 18

5(22 ~30? + 3F ~l8®5P(P‘W*5(F‘\0>

19) 9n2—37n+30

‘an ‘th “Fm + ’50n(61n—1o)-5(an—-Io)

21) 16,? + 10,124+ 40p+25

2‘91(8F+ 5 + 5(af>+5)

@—

23) 18p3—6p’tL3p-1

“F73?” +l(3f~1)

Solve each equation by factoring.

25) (a—2)(a+ 7)=o

18) 5m2—2m—3

5m2 ~5m + Em ‘ 5

5m(m- 1) WW“)

20) 9n2+15r1+4

22) 35a3 + 30114» Ma +12

531(15 Ho)+ 2(18 Ho)

24) 30v3 + ssvzl— 48v — 56

5V2(\0V +1)'8(bv +1)

(5V2-BXWH-‘O ' _

26) n(n-6)=0

0:0 n‘loib

27) (71+ 6)(n + 2) = o

H‘HD :0 “+220

29)b2—10b+21=0

bQ-Sb —1b+21= O

b(b—3)-1(b-3):o(b-3qul =0 »

31) x2+9x+20=0

x2 +5x + [ix +2020

x (we) HO! +6910

(¥+S)(X+°l) =0

Solve each equation with the quadratic formula.

33) 7x2+2x—21=0

2(1)

—2 «Hem.

F.b 1' Jébfg‘lol X- ’5)

Z "l

28) (k—2)2=0

K~2=O

[El

30) x2—3x—10=0

X2~5x +2x~107~0+2(a<~53=6

(x-53Cm23zo

32) x2—13x+40=0

x2-8x-6x +H0=C>

»<<><—8>-6<><~a>=o(x—93(><~E>3=0

34) 6r2—12r—8=0

36) 8b2+12b+2=0

-12 14122 “100(1)

2(8

mlb H

.4.

Describe the end behavior of each function.

37) f(x) =x3 — 3x2 38) )r(x)=—x3 +3):2 +1

@ L=60wn L‘ U?

12: 01> 2: down

39) f(x)=—x4+x2+x_4 40) f(x)=-x3+x2-3

L: down U Of

K'- down Q; down

OWrite a polynomial function that has the given zeros.

41) S, 1, 3, 4 42) 2mult.2, —3

41(X‘5XK‘1XX-3XX *4) 4.3)

43) —2, -3, S, O 44) 4mult.3

33(x+2)(x+ aXx-sXx) I ‘j 2 W403

63

=x2+6x+946) f (X)

IIIIIIIEIIIIIIIIIII-NMIIIIIIIIIIlung-IIIIIIIIIIIII-IIIIIIIIIIII

48) f(x) = —2x2 + 4x

XIll-Ill.

~2)<(x - 2)

0,2X

lo

Sketch the graph of each function.

x2+2x—3

— (x +2XX +10)

x=—2,-

-9<‘_’+2)<“—3X—lo4") J U}

Ul

\J

2

H.

.wx

L.

;llllllllllllllll.Wllllllllllllllll

X

llllllllllllllll\J

+.III-llllllllllll/\

u:

2lull

Ill-IIIIIIb

X

lull-lull..T

ulllllllllllllllll

L.

u]

+

,nmnuunnnunnuunnu.\1

X

.

3v_AIlmlulllaillllll

U1

VIA

1lull-Inullllulll

.T

10

1

__Ill-Illa

..lllllll

)Ill-III!

III-IIIVA

.T

VA

IVIII-lullanllllll

(

f

nnnunnuuuuuwna22

m.I!

X

/X\

05.r

\J

m

5

41.+

\J

2

VA

6.

mm

(0\

T

l.XS

3,.f/\..X

\J

\AUJ

I

7.

6l10...+I.

IV

2

:

f

VA

VA

)/\

VA.

N

2

/_\

o.

6..

Q

III...1II.I

IIIES “BII

I

X2(X+%)+ 109%)

(X2 +8)

>< = —3

Prove the function is even.

55) f(x)=x2+4x—S 56) f(x)=x2—6x+8 K?

¥(-><)=(-X)2+Ll(’1<)‘5 fox): (5x)2 ~lo(-x) +8= x2~L1x ~ 5 _ 2

— x Max +8

NO) @1010 ~ ‘NO)- ’6)!an

Prove the function is odd.

57) f(x)=x3+4x2—5x 58) f(x)=x3-—x2—20x

(1)3 + HWY-Sled 1+1) = ~60? 40(4)

3')(%+Ll)(2’r5>< _ “XE-X2120)! _

N61 006 MW 006 G)

59. The graph below Shows the curve that represents the low temperature for every day in January.

Temperature(Celsius)

MODEL 1:

(20, 0) Date

MODELZ: T 1 U9, 't

o .y. '5 CAI’ 'AI

Three different models have been proposed that could be used to

determine the January temperatures in one specific year. The

models are given below:

Model 1: y=ax2 + bx Hr

Model 2: y =(x—3)(x—9)(x—20) ,

Model 3: y = —x‘ +bx3 +cxz +dx+ e

None of these models are completely appropriate for this graph.

Explain what is incorrect with each model.

is ‘l

no

man

MODEL 3: i 5

60-64. Answer the following questions about the graph below.

60. Based on the end behavior, what type of degree is the polynomial (odd or even)?

‘LVP/F)

61. Is the leading coefficient of the polynomial negative or positive?

N213?) t'NxQ,62. What are the solutions to the polynomial?

"2,0,3

63. Given the solutions, write the equation of the polynomial in factored form

)5 = ><(><+2)()<~3)z

64. How many relative maxima and minima does f(x) have?

2 max’e and l min.!