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

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Question 36222: Can someone show me how to simplify this
(x^1/3 divided by x^5)^3
Click here to see answer by benni1013(197)

Question 36220: Please help me factor this-please show me the steps
3x^2 + 2x - 16
Click here to see answer by benni1013(197)

Question 36252: can someone answer this for me?
6x + 2y
is this:
monomial,binomial,triomial or not a polynomial?
Click here to see answer by Prithwis(166)

Question 36261: Simplify the complex fraction:
2/14x over 4/7xy
Click here to see answer by stanbon(57377)

Question 36192: Commuting students. At a well-known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students drive more than 40 miles daily, and 1/6 of the graduate students drive more than 40 miles daily. If there are twicde as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles daily?
Click here to see answer by mukhopadhyay(490)

Question 36291: What is the factored expression off 24x^3+18x^2
Click here to see answer by checkley71(8403)

Question 36221: Can someone show me how to simplify these 2 problems--please show me the steps
(2x)^2 * (3x^4)
and
(-3x divided by 2y^3)^-2

Click here to see answer by checkley71(8403)

Question 36309: please help me with this!
x squared -9x+14
Click here to see answer by checkley71(8403)

Question 36329: x^2-8x+15 / x^2 - 3x
Click here to see answer by vidhyak(94)

Question 36341: how do I find the constant of a polynomial y^3-4y^2+2y+9
Click here to see answer by ilana(307)

Question 36367: Help
RAtional Expression
3x^2-18x
________
-9x^2
-x^2/3x^2-18x/0+0
-0x^2
3x^2-18x
-0x^2
3x^2-18x
Click here to see answer by kirubakaran(5)

Question 36360: I wanted to check my work to make sure I did this correctly!
Rational Expression
15x/45 = x/3

Click here to see answer by benni1013(197)

Question 36398: find all rational zeros for p(x) x^3+5x^2+3x+7
Click here to see answer by stanbon(57377)

Question 36441: -7a^2/35a^8-28a^6-14a^3+21a^2
Click here to see answer by vidhyak(94)

Question 36440: -7a^2/35a^8-28a^6-14a^3+21a^2
Click here to see answer by vidhyak(94)

Question 36354: 5-x /x^2-8x+15
Click here to see answer by elima(1433)

Question 36361: Can someone help me solve please!
Rational Expression
x^2 -8x+15/(3x-15)
________________
x^2-3x
Click here to see answer by elima(1433)

Question 36355: x^3 +9x^2+14x/x^2-4
Click here to see answer by elima(1433)

Question 36457: add
y over y^2-49 + 7 over y^2+8y+7
show work
Click here to see answer by checkley71(8403)

Question 36475: Determine the roots of the following quadratic equation
x^2 - 14x + 45 = 0
Click here to see answer by vidhyak(94)

Question 36460: x^2=7x+10
Click here to see answer by Alwayscheerful(414)

Question 36476: The sum of the three sides of a triangular parcel of land is 451 yards. Assume that the lengths of the three sides are a, b and c, respectively. It is known that a is 31 yards shorter than b, while c is 66 yards longer than a. What are the lengths of the three sides?
Click here to see answer by Paul(988)

Question 36479: I am having trouble solving this, I have tried it up to the point where I need get the final answer but I have a feeling its wrong, Can you please check to see what I am doing wrong and help out

Divide:
2x^2 + 5x – 12/9x^2 – 16 ÷ 2x^2 – 7x + 6/3x^2 – x – 4

I inverted the divisor
2x^2 + 5x - 12/ 9x^2 - 16 ÷ 3x^2 - x - 4/2x^2 - 7x + 6

Now I am going to set it up to multiply the numerators and denominators
(2x^2 + 5x - 12)(3x^2 - x - 4)
(9x^2 - 16)(2x^2 - 7x + 6)
Now I am going to factor
(2x - 3)(x + 4) (3x^2 - x -4)
(3x + 4)(3x - 4)(2x - 3)(2x - 2)

I can only see one thing that will cancel out and that is the (2x - 3)
but I dont think the answer is
(x + 4)(3x^2 - x - 4)
(3x + 4)(3x - 4)(2x - 2)
I think I have missed a step here or I did not factor correctly, please help, I am having a hard time with this one.
Thank you very much!

Click here to see answer by rapaljer(4667)

Question 36477: how do you solve this? to simplify and factor and cancellation
x^35x^2+2x-8/x-1
Click here to see answer by rapaljer(4667)

Question 36470: Determine the GCF of the following terms:
54x^5 y^7 z^3 , 72x^3 y^5 z^2 , 63x^4 y^3 z^9
Click here to see answer by rapaljer(4667)

Question 36469: please help

y over y^2-49 + 7 over y^2+8y+7
show work
Click here to see answer by rapaljer(4667)

Question 36478: Marvin can shovel the driveway of his family home in 30 minutes. It takes his wife, Nina, 45 minutes to shovel the same driveway. How long would it take to shovel the driveway if they were both working together to clear it?
Click here to see answer by rapaljer(4667)

Question 36434: what is::
x squared minus x minus 12....................................x plus 3
____________________________ divided by _____________________________
..............6.........................................................x minus 4
Click here to see answer by rapaljer(4667)

Question 36219: Can someone show me how to factor this--please show me the steps-thanks
s^2 - 10s + 24

Click here to see answer by rapaljer(4667)

Question 36363: Check my Work Please!
Rational Expression
(x2 * x+2) / x
__ ___ __
5 2 30
(-18x^2)
________
(x+2)
Click here to see answer by elima(1433)

Question 36500: Can someone please help do this:
(4k + 7y)^2
Click here to see answer by elima(1433)

Question 36520: I need help figuring out how to do this problem, the square root of 2 time the square root of 8.
Click here to see answer by benni1013(197)

Question 36519: What is s^2-3s+3s-9?
Click here to see answer by benni1013(197)

Question 36518: What is 66ab+66ab?
Click here to see answer by benni1013(197)

Question 36502: Can someone please show me how to do this:
(s+3)(s-3)
Click here to see answer by benni1013(197)

Question 36501: Can someone please help me do this:
(6a + 11b)^2
Click here to see answer by benni1013(197)

Question 36499: Can someone please help me do this:
14m^2 + 23m - 15
I need to also find the GCF
Click here to see answer by checkley71(8403)

Question 36570: Hi
I am having a bit of trouble with this problem from my worksheet for pratice problems, any help would be greatly appreciated.
Divide and simplify:

3x^2 + 13x + 4/16 – x^2

÷

3x^2 – 5x – 2/3x – 12
I want to invert the divisor and multiply
so the new problem is

3x^2 + 13x + 4/16 – x^2

x(times)

3x – 12/3x^2 – 5x – 2

I cant seem to factor the 3x^2 + 13x + 4 =, is this possible, I have tried every combination of numbers but nothing is working.
I think the 3x – 12 can be factored down to 3(x – 4)
I think the 16 – x^2 should be switched to read –x^2 + 16 which can be factored down to –(x – 4)(x – 4)
I think the 3x^2 – 5x – 2 can be factored down to (3x + 1)(x – 2)

And I am stuck at this point, because I really think that the 3x^2 + 13 + 4 can be factored down to simpler terms to come up with the final answer
Please help?
Thank you very much!

Click here to see answer by stanbon(57377)

Question 36592: Determine the LCD of the following terms:
54x^5 y^7 z^3, 72x^3 y^5 z^2, 32x^4 y^3 z^9
Click here to see answer by rapaljer(4667)

Question 36591: Fill in the blanks:
a) For the expression 1 over the square root of x-2 to have real value, the value of X must be __________ than ________.
b) the LCD of 1 over x+1 and 3 over (x-1) is 1 over x^2 - 1. True or false?
c) 2x^2 + 13x - 34 = (__x + __) (x-__)
d) The equation 1/2 - 3 over 2x + 5 = 3/4 is equivalent to 4x - 2 = 6x + 15. True or False?
Click here to see answer by rapaljer(4667)

Question 36590: A carpet has the dimensions X feet by (X + 2)feet. If its area is 224 square feet, what are the dimensions of the carpet?
Click here to see answer by checkley71(8403)

Question 36574: I HAVE TO FACTOR THE POLYNOMIAL COMPLETELY. BUT I AM STUCK.
128xcubed yto the sixth - 50xto the sixth ycubed
it should look like this
128y3x6-50x6y3
WHAT DO I DO??PLEASE HELP ME. THANKS!
Click here to see answer by checkley71(8403)

Question 36631: While vacationing in the orient, Sonia spends $200 purchasing ornate cchess sets for her gift shop in California. A week later she finds the same chess set selling for $5 less per piece in the bazaars of Bombay. She spends another $150 purchasing some more sets in order to average down her cost/piece.
Write an algebraic expression for the total number of chess piecces Sonia has now.
Click here to see answer by Paul(988)

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