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