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

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Question 1002112: Find a 4th degree polynomial with zeroes of 2,-2,3i and f(0)=-108. Our math book doesn't explain anything on how to solve this, I have searched online and believe I have the solution. I want some verification if i am correct or not.
f(x)=(x-3i)(x+3i)(x+2)(x-2)
(x^2+9)(x^2-4)
(x^4-5x-36)
I am unsure for the rest. and what to do with f(0)=-108
Click here to see answer by ikleyn(52775)

Question 1002156: A quadratic equation whose roots are 1 and -5, and whose coefficient is 1
Click here to see answer by josgarithmetic(39616)

Question 1002172: find all numbers for which the following rational expression is undefined. If the rational expression is defined for all real numbers, state so.
5/(z-4)(z+2)
Click here to see answer by MathLover1(20849)

Question 1002278: This question is:
What is the slope of the line with the equation 2x + 3y +6 = 0
Click here to see answer by josgarithmetic(39616)

Question 1002232: Given that 3 is a zero of f(x)= x^3-7x^2+17x-15, find the other zeros using synthetic division. Simplify answers so that they are exact.
Click here to see answer by josgarithmetic(39616)

Question 1002340: X^2-13x+42 over
X^2-4x-21
Equals to what must be simplify

Click here to see answer by fractalier(6550)

Question 1002340: X^2-13x+42 over
X^2-4x-21
Equals to what must be simplify

Click here to see answer by stanbon(75887)

Question 1002346: Ok the question says, Which polynomial is equal to (-3x^2+2x-3) subtracted from (x^3-x^2+3x) ?
I keep getting an answer that's not on the list, so I just need help. My answer that I got was -x^3-2x^2-x-3. Which I don't see a negative answer starting with x^3 on my answer choices. Someone help me please Thanks
A. -2^3+2x^2+x-3
B. -2x^3+2x^2+x+3
C. x^3+2x^2+x-3
D. x^3+2x^2+x+3
Click here to see answer by josgarithmetic(39616)

Question 1002365: ((x^2)-(81))/((x^2)+(13x)+(42))
Click here to see answer by fractalier(6550)

Question 1002375: Which of the following is equal to (2x^3-3x^2+4x-3) subtracted from
(x^3-2x+5)?
I got x^3-3x^2+6x-8 ,
would it be C. x^3-x^2+6x-8 ?
A. -x^3-x^2-6x+8
B. -x^3+3x^2-6x+8
C. x^3-x^2+6x-8
D. x^3+x^2+6x-8
thank you
Click here to see answer by Boreal(15235)

Question 1002437: Find each product
1). (2m^2+n)(3n^2+6mn-m^2)
2). (4x-5)(2x^5+x^3-1)
thank you, show work please
Click here to see answer by MathLover1(20849)

Question 1002515: Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x)=11x^3-x^2+11x-1
1.)Find the real zeros of f
2.)Use the real zeros to factor f
Click here to see answer by stanbon(75887)

Question 1002500:

Jim travels
6 times faster than Brenda. Traveling in opposite directions, they are
392 miles apart after
3.5 hours. Find their rates of travel.

Click here to see answer by lwsshak3(11628)

Question 1002501: Consider the expansion of (x+y)^n.
1. How many terms does the expression contain?
2. What is the exponent of x in the first term?
3. What is the exponent of y in the first term?
4. What is the sum of the exponents in any term of the expansion ?
Show work please, thanks
Click here to see answer by KMST(5328)

Question 1002792: Use the given zero to find the remaining zeros of the function. h(x)=4x^4+7x^3+34x^2+63x-18; zero; -3i. Please show work.
Click here to see answer by solver91311(24713)

Question 1002839: If a strip of beach is cleaned in 4 hours, what part of the beach is cleaned in 1 hour?
Click here to see answer by ikleyn(52775)

Question 1002975: I need help with a homework problem from Saxon Algebra 1. (It is from Lesson 52, Practice #21 on page 333.) The problem states, "Find the excluded value in the expression b^5/b^3." I'm not sure about my guess. Is it 0? Thanks for taking the time to answer this :)
Click here to see answer by josgarithmetic(39616)

Question 1002914: zero of 0 and zero of 1 having multiplicity 2; f(2)=10
Click here to see answer by ikleyn(52775)

Question 1002917: zeros of -3,1, and 4;f(2)=30

a=-3 b=1 c=4
f(x)=(x+3)(x-1)(x-4)
Click here to see answer by ikleyn(52775)

Question 1002993: "A rectangular window has a length of (6a)/(3a-1) meters and a width of (4)/(3a-1) meters. How many feet of trim will be painted if the trim goes around three sides of the window (both lengths and one width)?"
Click here to see answer by Boreal(15235)

Question 1003123: A square picture is surrounded by a rectangular frame. The length of the framae's thickness is 8cm and the width's thickness is 6cm. The picture's side length is x. The total area is to be 320cm^2.
Find the side length of the picture (x).

Click here to see answer by josgarithmetic(39616)

Question 1003189: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 - 2x - 5
Click here to see answer by josgarithmetic(39616)

Question 1003361: If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a
Click here to see answer by mananth(16946)

Question 1003445: Find two consecutive positive odd integers whose product is 195 .
Click here to see answer by Alan3354(69443)

Question 1003444: Find three consecutive integers such that the product of the smaller and larger is one less than nine times the intermediate integer
Click here to see answer by stanbon(75887)

Question 1003400: The sum of an infinite geometric sequence is 9/7 and the first term is 1. Find the common ratio of the sequence.

A. 2/7
B. 2/9
C. 7/9
D. 2/9
E. 1/9
Click here to see answer by fractalier(6550)

Question 1003492: what is the awnser to k-1=3

Click here to see answer by ikleyn(52775)

Question 1003427: Find the real zeros of the polynomial function by factoring. The number in parentheses to the right of the polynomial indicates the number of real zeros of the given polynomial function. (Enter your answers as a comma-separated list.)
P(x) = x^3 − 3x^2 − 28x
(3)
x =

Click here to see answer by ankor@dixie-net.com(22740)

Question 1003421: Use long division to divide the first polynomial by the second.
8x3 + 9x^2 − 13x + 29, x + 4
Click here to see answer by josgarithmetic(39616)

Question 1003421: Use long division to divide the first polynomial by the second.
8x3 + 9x^2 − 13x + 29, x + 4
Click here to see answer by MathTherapy(10551)

Question 1003569: R^2 - 5r+6
-----------------(over)
R^2-4
For all r=positive and negative 2
Click here to see answer by KMST(5328)

Question 1001497: P(x) = 4x4 − x3 − 8x2 + 18x − 4
Find all the zeros of the polynomial function. (Hint: First determine the rational zeros. Enter your answers as a comma-separated list. Enter all answers including repetitions.)
x =
Write the polynomial as a product of its leading coefficient and its linear factors.
P(x) =

Click here to see answer by sidt36(1)

Question 1003614: Please help me solve the following: factor the polynomial...x^2 − 2x − 6
one zero is: c = 1 − square root of 7
*If one zero is 1-square root of 7 than the other is 1+square root of 7.
Though I don't remember how to factor this. Please help me and show work so that I can figure it out for the rest of the homework.
Thank you!
Click here to see answer by stanbon(75887)

Question 1003702: Explain why can not be simplified to
Thanks in advance to anyone who can help! :)
Click here to see answer by josgarithmetic(39616)

Question 1003702: Explain why can not be simplified to
Thanks in advance to anyone who can help! :)
Click here to see answer by KMST(5328)

Question 1003716: when a polynomial P(x) is divided by 3x-4, the quotient is x^3+2x+2 and the reminder is -1. Find P(x).
Click here to see answer by ikleyn(52775)

Question 1003703: Which expression is not equivalent to ?
A:
B:
C:
D:
Click here to see answer by josgarithmetic(39616)

Question 1003762: I know that someone has already answered this question. but i didn't understand it.
Find the value of x in this diagram.
http://imgur.com/IbkSbNZ
Please explain the steps. Thanks
So the person stated that both "triangles" have the similar ratios. I don't understand how they got that. Please explain or solve it another way. (i tried to solve it using Pythagoras, but didn't get the answer right [x=2])
Click here to see answer by Edwin McCravy(20054)

Question 1003893: Find a polynomial of lowest possible degree that has 2 as a zero of multiplicity 3, and -1 as a zero of multiplicity 1.
Click here to see answer by MathLover1(20849)

Question 1003892: Find a polynomial with real corfficients that has -2 and 2 + i as zeros
Click here to see answer by ankor@dixie-net.com(22740)

Question 1003892: Find a polynomial with real corfficients that has -2 and 2 + i as zeros
Click here to see answer by jim_thompson5910(35256)

Question 1003897: Given that a-3b/a+2b=3, find the value of a+3b/a-2b. Express your answer as an integer or common or improper fraction reduced to lowest terms. Do not use decimals.

Click here to see answer by Boreal(15235)

Question 1003914: Find a polynomial with integer coefficients that has 1/4 and −√2i as zeros.
Click here to see answer by josgarithmetic(39616)

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, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 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