Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

Tutors Answer Your Questions about Polynomials-and-rational-expressions (FREE)

Question 1099167: P(x) = x4 − 6x3 + 38x2 − 80x + 200; 2 + 4i
Click here to see answer by ikleyn(52769)

Question 1099166: P(x) = x4 − 10x3 + 35x2 − 10x + 34; 5 − 3i
Click here to see answer by Alan3354(69443)

Question 1099193: Solve each equation
Click here to see answer by richwmiller(17219)

Question 1099204: P(x) = x4 − 6x3 + 38x2 − 80x + 200; ��2 + 4i
Use the given zero to find the remaining zeros of the polynomial function.

Click here to see answer by josgarithmetic(39615)

Question 1099205: According to the Intermediate Value Theorem, if a polynomial has points: (0,10) and (6,-8)
a) f(2) is a value between 0 and 6
b) f(3) is a value between 10 and -8
c) f(4) is not a value between 0 and 6
d) f(5) is not a value between 10 and -8
(Homeschooling mother trying to help daughter with this problem. Thank you)
Click here to see answer by themasterofcircuits(27)

Question 1099265: Find a polynomial with integer coefficients that satisfies the given conditions:
P has a degree 2 and zeros and
I tried multiple times to get the formulat right, Im sorry I cant figure it out.
Click here to see answer by Fombitz(32388)

Question 1099268: A) Factor the Polynomial Completely
P(x)= x^3 - 3x^2 + 4x
B) Find all its zeros. State the multiplicity of each zero. (order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part)
Click here to see answer by Fombitz(32388)

Question 1099266: A) Factor the Polynomial Completely
P(x)= 81x^4 -625
B) Find all its zeros. State the multiplicity of each zero. (order your answers from smallest to largest real, followed by complex answers ordered smallest to largest real part, then smallest to largest imaginary part)
Click here to see answer by Boreal(15235)

Question 1099282: Factor the Polynomial completely
p(x)= x^5+6x^3+9x
Find all its zeros. State the multiplicity of each zero.
Im specifically not understanding how to fund multiplicity, so please dont forget that part.
Click here to see answer by ikleyn(52769)

Question 1099280: Find a polynomial with integer coefficients that satisfies the given conditions.
U has degree 5, zeros 1/2, −4, and −i, and leading coefficient 4; the zero −4 has multiplicity 2.
Click here to see answer by KMST(5328)

Question 1099337: Solve the equation and check your solution: +=

I really do not understand this problem. If you just tell me how to solve it I will solve it myself, but I'm completely at a loss as to how to start.

Thank you in advance.
Click here to see answer by Alan3354(69443)

Question 1099335: Factor 54k^3m-16m^3

You can factor out a 2m and make it 2m(27k^3-8m^3), right? But is that it? Can it be factored more?

Thank you in advance.
Click here to see answer by josgarithmetic(39615)

Question 1099332: Find the area of an oak cabinet that is a large square with sides of 6x feet and has a square cut-out region whose sides are y feet. Write your answers in factored form.
I think the equation is 6x⋅6x-y⋅y or 6x^2-y^2, but I'm not entirely sure if that is right or how to put it in factored form.

Thank you in advance for your help!
Click here to see answer by Theo(13342)

Question 1099422: For the polynomial below, -2 is a zero. h(x)=x^3+8x^2+14x+4
Find the other zeros.
Click here to see answer by josgarithmetic(39615)

Question 1099422: For the polynomial below, -2 is a zero. h(x)=x^3+8x^2+14x+4
Find the other zeros.
Click here to see answer by Edwin McCravy(20054)

Question 1099516: An object is thrown straight up into the air then follows a trajectory , the height s(t)of the object is given by the function s(t)=4t-16t�
1)what is the maximum height reached by the object?
2)how long did the object reached its maximum height?
This is trajectory topic
Click here to see answer by ikleyn(52769)

Question 1099577: Can someone please describe and correct the error of the following equation.
(3x-2)(2x-3)
=3x(2X-3)-2(2x-3)
=6x^2-9x-4x-6
=6x^2-13x-6
I think that the 4x should have been subtracted from the 9x.
Thanks.
Click here to see answer by Fombitz(32388)

Question 1099605: 32x^3-40x^2-76x-24/8x+4
Click here to see answer by ikleyn(52769)

Question 1099606: 32x^3-40x^2-76x-24/8x+4
Click here to see answer by richwmiller(17219)

Question 1099606: 32x^3-40x^2-76x-24/8x+4
Click here to see answer by josgarithmetic(39615)

Question 1099591: if alpha,beta,gamma,and delta(symbols) are the roots of x^4-2x^3+4x^2+6x-21=0 if alpha + beta =0, solve the equation completely.
Click here to see answer by ikleyn(52769)

Question 1099740: Find a Fourth- degree polynomial with interger coefficients that has zeros 5i and -1, with -1 a zero of multiplicity 2.
My answer was (x-5i)(x+5i)(x-1)(x-1), but its wrong. I dont know what I did wrong
Click here to see answer by Alan3354(69443)

Question 1099745: Find the complete factorization of p(x)= x^4-2x^3+10x^2-18x+9

Click here to see answer by Alan3354(69443)

Question 1099745: Find the complete factorization of p(x)= x^4-2x^3+10x^2-18x+9

Click here to see answer by ikleyn(52769)

Question 1099545: An amusement park owner wants to add a new wilderness water ride to his park. The ride includes a mountain that is in the shape of a square based pyramid. Before building the attraction, engineers must build and test a scale model.
(a) If the length of the sides of the base of the scale model of the pyramid is xcm and the height of the pyramid is 9cm less than the length of the sides of the base, write down an equation for the volume of the pyramid in terms of x.
You may assume that the volume of a square based pyramid is
V = 1Bh, where B is the area of the base and h is the height of the pyramid.
(b) If the volume of the model of the pyramid is 6300cm3, show that
x^3-9x^2-18900=0
(d) Fully factorise p(x) and hence explain why the base of the model pyramid has sides of length 30cm.
(e) If the model of the pyramid is built to a scale of 4:250, determine the height of the pyramid to be built
in the park.
Click here to see answer by htmentor(1343)

Question 1099893: use the given zero (4-3i) to fine the remaining zeros of the polynomial function P(x)=x4 − 8x3 + 26x2 − 8x + 25
Click here to see answer by josgarithmetic(39615)

Question 1099931: 9x^2+39-14 I have to factor using ac method
Click here to see answer by ankor@dixie-net.com(22740)

Question 1099933: 10x^5+11x^4+3x^3 I have to factor by grouping and ac method please help I don�t know what I�m doing wrong
Click here to see answer by KMST(5328)

Question 1100132: Form a polynomial whose real zeros and degree are given.
Zeros: -1, 0, 3; degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1.
y =
Click here to see answer by richwmiller(17219)

Question 1100329: Explain why 2 + 3(x � 2) = 5x � 10 is not true as a rule.
Click here to see answer by josgarithmetic(39615)

Question 1100329: Explain why 2 + 3(x � 2) = 5x � 10 is not true as a rule.
Click here to see answer by ikleyn(52769)

Question 1100353: Suppose f(x) is a polynomial. What is the least possible degree of that polynomial?
x: -24 -18 -12 -6 0 6 12 18 24
f(x): -8 -1 3 -2 4 7 -1 -8 5
Click here to see answer by greenestamps(13198)

Question 1100423: Form the fifth-degree polynomial function with real coefficients,
given that 1+i is a zero, and that the graph passes through (-2,0),
(0,8)(1,0)
Click here to see answer by Fombitz(32388)

Question 1100632: solve X for X^(2n)-1<0
Click here to see answer by Fombitz(32388)

Question 1100632: solve X for X^(2n)-1<0
Click here to see answer by Alan3354(69443)

Question 1100701: write a polynomial function f(x) of degree 3 with integer coefficients and zero of 6i and 4/5.
Click here to see answer by josgarithmetic(39615)

Question 1100915: In a 18-inch square television set, the length of the screen�s diagonal is 18 inches. Find the measure of the side of the screen.

Click here to see answer by Alan3354(69443)

Question 1100942: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i
Click here to see answer by stanbon(75887)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 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20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105