18 Polynomial factors and graphs.docx
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18Polynomialfactorsandgraphs
Polynomialfactorsandgraphs
1.P（x）=2x3−18x
Giventhepolynomialfunction P definedabove,whatareitszeros?
A.{−9,−6,2,3}
B.{−9,0,2}
C.{−3,3}
D.{−3,0,3}
CorrectAnswer:
DDifficultLevel:
2
2.WhichofthefollowingfunctionscouldrepresentthegraphBELOWinthexy-plane,wherey=P（x）?
A.P（x）=x2+6x+8
B.P（x）=x3+6x2+8x
C.P（x）=x2−6x+8
D.P（x）=x3−6x2+8x
CorrectAnswer:
BDifficultLevel:
2
3.Apolynomialhaszerosat −9, 2,and 0.Whichofthefollowingcouldbethepolynomial?
A.x2−7x−18
B.x3+7x2−18x
C.x3+7x2−18x
D.x3+6x2−25x+18
CorrectAnswer:
BDifficultLevel:
2
4.（x−7）（x+5）（2x−3）
Giventhepolynomialabove,whatareitszeros?
A.｛-7,5,-3｝
B.{7,-5,3}
C.{-7,5,-
}
D.{7,-5,
}
CorrectAnswer:
DDifficultLevel:
2
5.2（x+55）（x−17）
Giventhepolynomialabove,whatareitszeros?
A.x=−55 andx=17
B.x=−55,x=−2,andx=17
C.x=−17 andx=55
D.x=−17, x=2,andx=55
CorrectAnswer:
ADifficultLevel:
2
6.G（z）=（z−1）5−（z−1）4Thepolynomialfunction G isdefinedabove.Whatistheproductofthezerosof G?
Fillintheblank:
CorrectAnswer:
2DifficultLevel:
2
7.Thepolynomialfunction P haszerosat 3 and 6.WhichofthefollowingcouldbethedefinitionofP?
A.P（x）=x2+9x+18
B.P（x）=x2−9x+18
C.P（x）=x2+3x+6
D.P（x）=x2+6x+3
CorrectAnswer:
BDifficultLevel:
2
8.Whichofthefollowingequationscouldrepresentthegraphbelowinthexy-plane?
I.y=（x−3）（x+3）
II.y=（x−4）2
III.y=（x+2）（x+7）
A.Ⅰonly
B.Ⅱonly
C.IandⅢonly
D.I,ⅡandⅢ
CorrectAnswer:
ADifficultLevel:
2
9.h（t）=（t−8）1（t−4）2（t−2）3（t−1）4
Thepolynomialfunction h isdefinedabove.Howmanydistinctzerosdoes h have?
CorrectAnswer:
4DifficultLevel:
2
10.x3+25x2+50x−1000
Thepolynomialabovehas （x−5） and（x+10） asfactors.Whatistheremainingfactor?
A.（x+2）
B.（x-2）
C.（x+2）
D.（x-20）
CorrectAnswer:
CDifficultLevel:
2
11.x3+7x2−36
Thepolynomialabovehaszerosat −6 and 2.Iftheremainingzerois z,thenwhatisthevalueof−z?
CorrectAnswer:
3DifficultLevel:
3
12.Thefunction p isapolynomialof t suchthat（t−10）,（22−t）, （t+10）,and（20+t） areallfactorsof p（t）.Whichofthefollowingcouldbethegraphof y=p（t） inthe typlane?
A.
B.
C.
D.
CorrectAnswer:
ADifficultLevel:
3
13.Whichofthefollowinggraphsappearstorepresentapolynomialfunctionwithadoublezero?
A.
B.
C.
D.
CorrectAnswer:
DDifficultLevel:
3
14.g（x）=x4−4x3+6x2−4x+1
Thefunction g isdefinedabove.Giventhatallzerosof g areintegersbetween−1 and 1inclusive,howmanydistinctzerosdoes g have?
CorrectAnswer:
1DifficultLevel:
3
15.x2−ax+24
Ifoneofthezerosofthepolynomialaboveis 8,whatistheotherzero?
CorrectAnswer:
3DifficultLevel:
3
16.Forafunction g,thegraphof y=g（x）y=g（x） isshownBELOW.When g（x） isdividedby （x+10）,theremainderis −20.Whichofthefollowingisclosesttotheremainderwhen g（x） isdividedby （x−10）?
A.-28
B.-2
C.2
D.28
CorrectAnswer:
CDifficultLevel:
3
17.Thepolynomialfunction f isdefinedas f（c）=（c−k）（c2−4c+4） where k isaconstant.Thevalue 2 isazeroof f.Whatistheremainderoff（c） whendividedby （c−2）?
CorrectAnswer:
0DifficultLevel:
3
18.Whichofthefollowinggraphsinthe xy-planehave −3 and 5 asalloftheirdistinctzerosfor−6≤x≤6 ?
I.
II.
III.
A.Ionly
B.IandIIonly
C.IIandIIIonly
D.I.IIandIII.
CorrectAnswer:
BDifficultLevel:
3
19.Givensomerationalconstant a,whichpolynomialequationcouldrepresentthegraphBELOWinthe xy-plane?
A.y=a（x+1）2（x−5）
B.y=a（x+1）（x−5）
C.y=a（x+1）（2x+1）（x−5）
D.y=a（x−1）（x+5）2
CorrectAnswer:
BDifficultLevel:
3
20.Theequation s=（t+3）2（t+2）（t+1）（t）（t−1） isgraphedonthe stplane.Whatistheproductofthe tinterceptsofthegraph?
CorrectAnswer:
0DifficultLevel:
3
21.q（v）=（v−8）（v−5）（v−4）（v+5）（v+10）
Thefunction q isdefinedabove.Ifthesumofthezerosof q is s,whatisthevalueof s?
CorrectAnswer:
2DifficultLevel:
3
22.（x−√3）2（x−√7）
Giventhepolynomialabove,whatareitszeros?
A.x=−√3 andx=−√7
B.x=√3 and x=√7
C.x=3 andx=√7
D.x=−3 and x=−√7
CorrectAnswer:
BDifficultLevel:
3
23.Thegraphofthepolynomialequationy=α（t） isshownBELOW.Whichofthefollowingmustbetrue?
A.Theleadingcoefficientispositive.
B.Thesumofthedistincttinterceptsisnegative.
C.Theconstantcoefficientispositive.
D.Theproductofthedistincttinterceptsisnegative.
CorrectAnswer:
DDifficultLevel:
3
24.Thegraphshownatleftcouldrepresentwhichofthefollowingequations?
A.h=−（b−10）（b−20）（b+20）
B.h=（b−10）（b−20）（b+20）
C.h=−（b+10）（b−20）（b+20）
D.h=（b+10）（b−20）（b+20）
CorrectAnswer:
ADifficultLevel:
3
25.x3+7x2−36
Thepolynomialabovehaszerosat −6 and 2.Iftheremainingzerois z,thenwhatisthevalueof−z?
CorrectAnswer:
3DifficultLevel:
3
26.Thepolynomialfunction f isdefinedas f（m）=（m3−m2−17m−15）（m+1）.Whenf（m） isdividedby（m+1）,whatistheremainder?
CorrectAnswer:
0DifficultLevel:
4
27.p（n）=（n3−12n2+47n−60）（n−4）
q（n）=（n+13）（n−4）
Thefunctions p and q aredefinedabove.Oneofthefunctionshasazeroatn=5.Whatis（p+q）（5）?
CorrectAnswer:
18DifficultLevel:
4
28.WhichofthefollowingcouldbetheequationcorrespondingtothegraphBELOW?
A.s=a⋅a⋅a⋅a
B.s=（a−1）（a−1）
C.s=a⋅a⋅a⋅a⋅a
D.s=（a−1）（a−1）（a−1）
CorrectAnswer:
CDifficultLevel:
4
29.p=（w−30）（w2+178w+7921）
Giventhat −89 isadoublezeroofthepolynomialequationabove,whichofthefollowingcouldbethegraphoftheequationinthe pwplane?
A.
B.
C.
D.
CorrectAnswer:
DDifficultLevel:
4
30.ℓ（x）=x4+36x2−10,000
Thepolynomialfunction ℓ isdefinedabove.Whatistheremainderof ℓ（x） whendividedby（x+10）?
CorrectAnswer:
3600DifficultLevel:
4
31.g（w）=（w+13）3（w+19）2
Thepolynomialfunction g isdefinedabove.When g（w） isdividedby （w+16）,theremainderisr.Whatisthevalueof ∣r∣?
CorrectAnswer:
243DifficultLevel:
4
32.Afunction pp isdefinedas p（x）=（x−a）（x−15）（x−20）+15 where a isaconstant.Giventhat p（7）=15,whatisthevalueof a?
CorrectAnswer:
7DifficultLevel:
4
33.Afunction w isadefinedasw（x）=ax2+bx+c where a, b,and c areconstants.If a=3and w（3）=w（15）=0,thenwhatistheabsolutevalueof b?
CorrectAnswer:
54DifficultLevel:
4
34.Afunction s isdefinedass（x）=（x−4）（x−5）2.Afunctionh isdefinedash（x）=（x−a）s（x）.Forsomeconstant a, （x−a）3 isafactorof h.Whatis s（a）?
CorrectAnswer:
0DifficultLevel:
4
35.12x2+ax+2
Ifoneofthezerosoftheabovepolynomialis
,whatistheotherzero?
CorrectAnswer:
DifficultLevel:
4
36.Foranypolynomialfunction h,thepolynomialfunction g isdefinedtobeg（w）=（w−25）（w−1）h（w）.If h haszerosat 1 and 3 only,whatisthesumofthedistinctzerosof g?
CorrectAnswer:
36DifficultLevel:
4
37.Thepolynomialfunction ff isdefinedasf（x）=（x−c1）（x−c2）（x−c3）⋯（x−cn） forsomepositiveinteger n.Eachofthevalues c1, c2, c3,,, cn isarealnumber.Thegraphof y=f（x） isshownBELOW.Whichofthefollowingcouldbethevalueof n?
A.0
B.1
C.2
D.3
CorrectAnswer:
DDifficultLevel:
4
38.Thepolynomialfunction f isdefinedasf（m）=（m3−m2−17m−15）（m+1）.Whenf（m） isdividedby（m+1）,whatistheremainder?
CorrectAnswer:
0DifficultLevel:
4
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