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

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

Question 407312: Can someone please help?
Andrew factored the expression 54x^3-30x^2+15x as 5x(9x^2-6x+3). But when melissa applied the distributtive law at multiplied out 5x(9x^2-6x+3), she got 45x^3-30x^2+15x; thus, Andrews solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If prime state this.
Click here to see answer by jim_thompson5910(28598)

Question 406969: i dont understand how to do general factoring & its application of factoring by grouping. here is 1 of my problems;7(r-s)+t(r-s)
Click here to see answer by ewatrrr(10682)

Question 406969: i dont understand how to do general factoring & its application of factoring by grouping. here is 1 of my problems;7(r-s)+t(r-s)
Click here to see answer by jim_thompson5910(28598)

Question 407321: 1. In solving the equation (x + 1)(x – 2) = 4, Eric stated that the solution would be
x + 1 = 4 => x = 3
or
(x – 2) = 4 => x = 6
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.

Click here to see answer by richard1234(5390)

Question 406943: Perform the indication operations, and simplify if possible.
3x-7/x^2-9 - x-1/x^2-9
Click here to see answer by ewatrrr(10682)

Question 407015: Please help,
factor the expression 81a^2-36ab+4b^2 into a product of binomials.

Click here to see answer by ewatrrr(10682)

Question 407015: Please help,
factor the expression 81a^2-36ab+4b^2 into a product of binomials.

Click here to see answer by jim_thompson5910(28598)

Question 407436: I am needing help on this problem for my kids' homework.
SHOW ALL WORK: Factor out the GCF from the expression:
10 a^3 b - 2 a^2 b^2 - 8 ab^3
Click here to see answer by Alan3354(30993)

Question 407530: x^2-12x+20
It's asking me to factor this
and that is x squared minus 12x plus 20
Click here to see answer by jim_thompson5910(28598)

Question 407669: factor each polynomial, if possible. if the polynomial cannot be factored using integers, write prime a^2-11ab+18b^2
Click here to see answer by scott8148(6628)

Question 407814: I am looking for help on my algebra problem.
Completly factor the following expression and show all work: 49y^2-81z^2
Click here to see answer by stanbon(57424)

Question 407816: Can someone please help, I am trying to help my child with algebra homework and I have no idea what I am doing on this problem. I do know A=L*W, but that is as far as I can remember with this stuff. Thank you.
The length of a rectangle is 2 meters more than it's width. If the area is 63 sq meters, what are the length and width?
Click here to see answer by stanbon(57424)

Question 407813: I am looking for help on my algebra problem.
Completly factor the following expression and show all work: 81x^2-198xy+121y^2
Click here to see answer by stanbon(57424)

Question 407812: I am really needing help with this algebra problem, please help?
Use the "difference of squares" rule to factor the following expression:
9x^4-25y^2

Click here to see answer by stanbon(57424)

Question 407811: I am struggling with this problem, Can someone please help?
Megan factored the expression 28x^2-25x+3 as (7x-3)(4x-1). But when Jacob applied the FOIL principle and mulitiplied out (7x-3)(4x-1), he got 28x^2-19x+3; thus, Megan's solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
Click here to see answer by MathLover1(6649)

Question 407841: factoring 3x^2-5x-884
Click here to see answer by jim_thompson5910(28598)

Question 407821: I am needing help please.
Completly factor the expression and show all work:
245x^3-420x^2y+180xy^2
Click here to see answer by jim_thompson5910(28598)

Question 407843: 1. -6x + 23x +6
I don't understand polynomials at all. If this could be broken down so I can understand it, I'd appreciate it.
Click here to see answer by jim_thompson5910(28598)

Question 407842: factoring 3x^2-5x-884
Click here to see answer by Alan3354(30993)

Question 407820: I am needing help please.
Completly factor the expression and show all work:
18x^2-32y^2
Click here to see answer by jim_thompson5910(28598)

Question 407891: How do you divide 5x + 6x³ - 8 divide by x - 2
Click here to see answer by Edwin McCravy(8924)

Question 407818: I am looking for some help with this math problem. Thank you.
A 5ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 1 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
Click here to see answer by ankor@dixie-net.com(15667)

Question 407966: name the type of polynomial -10xy
Click here to see answer by Alan3354(30993)

Question 408002: Why is 9 a polynomial?
Click here to see answer by Edwin McCravy(8924)

Question 408017: x^2-4x 7x-30
---------- - ---------
(x-5)(x+6) (x-5)(x+6)
Click here to see answer by mananth(12270)

Question 408066: how many grains of sand are in a one quart mason jar?
Click here to see answer by solver91311(16897)

Question 408168: divide and simplify.

r^2+4r / r^2+2r-8 divided by r / r+2
Click here to see answer by ewatrrr(10682)

Question 408155: one half y squared minus 8 y + 32=0
Click here to see answer by checkley79(3056)

Question 408271: Can someone please help?
Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. Please show all work.
x + 9y = -26
-2x + 4y = -36

Click here to see answer by stanbon(57424)

Question 408272: Hi, I finished this equation and would like to know if you would check it for me? Did I do it right, if not, where did I go wrong?
(n)/(2)-(1)/(3)=13/6
common demonminator 6, multiply it
6(n)/(2)- 6(1)/(3)= 6 (13)/(6)
3n-2=13
+2 +2
(3n)/(3n) = (15)/(3)
n=5

Click here to see answer by stanbon(57424)

Question 408270: Can someone please help?
Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.Show all work
10x – 4 = 2y
2y – 10x = 2

Click here to see answer by stanbon(57424)

Question 408275: Hi, I finished this equation and was not sure about to simplify the final answer. Would you check it for me and show me how to do it? Thanks.
(x+2)/(3)+(x-1)/(4)=(9)/(2)
Common denominator is 12 and mulitply by it
12 (x+2)/(3)+ 12 (x-1)/(4) = 12 (9)/(2)
4x+2+3x-1=54
4x+3x+2-1=54
7x+1=54
-1 -1
(7x)/(7x) = (53)/(7)
x = 7 (4)/(7)

Click here to see answer by stanbon(57424)

Question 408282: Hi, I finished this equation and would like to know if you would check my answer. My textbook answer is says 1 but I got 1 (1)(11). I would like to know how to do the problem correctly. Thanks.
(c+5)/(7)+(c-3)/(4)=(5)/(14)
common demoninator 28 and multiply by it.
28 (c+5)/(7)+ 28(c-3)/(4)= 28(5)/(14)
4c+5+7c-3=10
11c+2=10
-2 +2
(11c)/(11c)=12/11
c=1 (1)/(11)
Click here to see answer by stanbon(57424)

Question 408287: Hi, would you check my work to see if I am doing it right and confirm the answer? Thanks.
-3(2t-5)=2(4t+7)
-6t-(-15)=8t+14
-6t-15-8t -8t
-14t-15=14
+15 +15
(-14t)/(-14t)=(29)/(14)
x=(29)/(14)

Click here to see answer by ankor@dixie-net.com(15667)

Question 408277: Hi, would you tell me where I went wrong? My textbook answer should be -12 but I came up with -6?
(n-3)/(2)-(4n-1)/(6)=(2)/(3)
Common denonimator 12 and multipy by it
12 (n-3)/(2)-12(4n-1)(6)=12(2)/(3)
6n-3-8n-1=8
-2n-(-4) =8
+4 +4
(-2n)/(-2n)=(12)/(-2)
n=-6
Click here to see answer by richard1234(5390)

Question 408268: I am looking for help, Please.
SHOW ALL WORK: If a stone is tossed from the top of a 190 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 190, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
Click here to see answer by josmiceli(9698)

Question 408269: Can someone please help?
Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
25x2 = 10x – 1

Click here to see answer by richard1234(5390)

Question 408266: I am needing some help Please.
In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be
x + 3 = 48 => x = 45
or
(x + 1) = 48 => x = 47
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning. Please show all work.
Click here to see answer by richard1234(5390)

Question 408295: what is the answer to the following problem. (3x-4)(5x-7).
Click here to see answer by algebrahouse.com(1079)

Question 408655: Degree of a polynomial ---
I don't understand how to find the degree of a polynomial --- if the equation is 9x^2 + yz^8 the answer book says "9" -- when I add them I get "11"
the x has 2, the y has 1 and the z has 8, so to my way of thinking 2 + 1 + 8 = 11
--can you explain how to find the answer? Thank you for your help....
Click here to see answer by stanbon(57424)

Question 408664: 8z^3-64=0
and its asking for possible 3 answers
Click here to see answer by richard1234(5390)

Question 408651: FACTOR 5W^2+19W+12
Click here to see answer by robertb(4012)

Question 408618: suppose that the coefficients of the equation p(x)=ax^3 + bx^2 +cx + d=0
satisfy the equation a + b + c + d =0
name a zero of the equation
Click here to see answer by richard1234(5390)

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