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

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

Question 250263: Suppose x^2 + bx + c has zeros r1 and r2, what is the polynomial in factored form multiplying the factored form out. What are then the relationships between this product and the coefficients in the original polynomial?
Click here to see answer by drk(1908)

Question 253266: Can someone help me! I keep getting two different answers to this problem (3a^3+4a^2-a-1)(a-5) My two answers are 3a^4-15a^3+4a^3-21a^2+4a+5 and 3a^4-11a^3-21a^2+4a+5 I want to lean more towards the bottom answer but I've used the calulater to a problem and it gave me the top answer.
Click here to see answer by jim_thompson5910(28595)

Question 253357: How can I factor the polynomial: 4x^4-5x^2-9 ?
Click here to see answer by Greenfinch(383)

Question 253402: if the domain of f(x)=4x^2-4x-2 is (-7,-5,-3,-1,1,2,3,4,6) what is the range ?
Click here to see answer by edjones(7569)

Question 253397: simplify: 1/x+1
------
1/x-1
Click here to see answer by edjones(7569)

Question 253462: find the rational roots of the equation 9x^4=12x^3+13x^2-12x+4=0
Click here to see answer by richwmiller(9135)

Question 253517: Factor the polynomial.
15x3y3+10x2y2+5xy
Click here to see answer by richwmiller(9135)

Question 253572: Please help me with this problem.
Look at the expression 4x-12/x^2-16. If x was replaced with 3, would the expression be considered defined? Why or why not? If x was replaced with 4, would the expression be considered defined? Why or why not? Is there another value for x that would make this expression undefined?
Click here to see answer by solver91311(16885)

Question 253595: Find the inverse of f(x)= 4-3x^3
Click here to see answer by jim_thompson5910(28595)

Question 253634: Can you help me factor each of the following completely?
1. 4x^2-48x+135

Click here to see answer by jim_thompson5910(28595)

Question 253634: Can you help me factor each of the following completely?
1. 4x^2-48x+135

Click here to see answer by richwmiller(9135)

Question 253630: For p(x)= 4x^5 + 4x^4 + 25x^3 - 56x^2 - 74x - 20
a. Factor into linear and irreducible quadratic factors
b. Factor completely
c. Find all zeros
Click here to see answer by drk(1908)

Question 253560: Tell whether the expression is a Polynomial. If it is a polynomial, find its degree and classify it by the number of it's terms. 3m^-5+9
Click here to see answer by stanbon(57342)

Question 253740: Please help me solve x²-3xy+2y²
,Thanks
Click here to see answer by richwmiller(9135)

Question 253767: plese Simplify the following and state the degree of the resulting polynomial: ( x 3 + 3x + 2) * ( x + 1) – ( x 4 + x 2 + 2x).
Click here to see answer by MRperkins(300)

Question 253704: Please help me solve this equation: (6x^-4x=7)+(2x^-3x-9)=
Click here to see answer by richwmiller(9135)

Question 253747: Please help me solve:
1) x²+x-72
2) x²-15x+156
3) x²-6x-16
,Thanks
Click here to see answer by drk(1908)

Question 253747: Please help me solve:
1) x²+x-72
2) x²-15x+156
3) x²-6x-16
,Thanks
Click here to see answer by richwmiller(9135)

Question 253825: a2+17a+72
Click here to see answer by drk(1908)

Question 253825: a2+17a+72
Click here to see answer by richwmiller(9135)

Question 253891: how would i factor (x + 2y) squared - 3(x+2y) +2

Click here to see answer by stanbon(57342)

Question 253891: how would i factor (x + 2y) squared - 3(x+2y) +2

Click here to see answer by richwmiller(9135)

Question 253891: how would i factor (x + 2y) squared - 3(x+2y) +2

Click here to see answer by jim_thompson5910(28595)

Question 253899: Look at the trinomial below.
x^2 + 8x + 15
Factor the trinomial as the product of two binomials.

I think the answer is (x+3)+ (x+5)
Is this correct.
Part B
Use what you know about binomials and trinomials to explain how you found
the answer.
I don't know how to answer this.
Part c
supppose the middle term of the trinomial had been -8x instead of 8x. How would
the factored form change? __________________________I think it would be
negative.
Click here to see answer by jim_thompson5910(28595)

Question 253921: I have not seen this written out in words like this before. I have the answer but don 't know how they got it. the question is: which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x? the answer is 6x^2-5x-6.
Click here to see answer by richwmiller(9135)

Question 253943: it says for all r, then has an = sign with a line thru it, +_ 2. so not equall to and plus or minus to 2? r^2-5r+6 over r^2-4. answer is r-3 over r+2. not sure how to get this answer. Thanks!
Click here to see answer by jim_thompson5910(28595)

Question 254062: Please help me to solve this problem
*one factor 6xcube + 6xsquare - 2x - 2 is 3xsquare - 1. What is the other factor?
Click here to see answer by richwmiller(9135)

Question 254053: Patricia and chelsea can build a bike together in an hour and a half. However, if Patricia worked with Tanesha they can build the same bike 10 minutes faster. Working by herself, Patricia can build a bike 2 hours faster than Tanesha.
a) How long will it take for each girl to build a bike by herself?
b) How long will it take for the three of them to build a bike together
Click here to see answer by palanisamy(496)

Question 254239: Translate the following sentence into an equation: the quotient of (x + 3) and 5y is the same as the product of x and y.
Click here to see answer by richwmiller(9135)

Question 254242: 3x2 plus kx plus 4 divided by x-2=3x-2 then k= , if x= (with a slash mark going thru = sign)
Click here to see answer by MRperkins(300)

Question 254242: 3x2 plus kx plus 4 divided by x-2=3x-2 then k= , if x= (with a slash mark going thru = sign)
Click here to see answer by drk(1908)

Question 254252: n – 0.7 = -1.2
Click here to see answer by richwmiller(9135)

Question 254270: I dont know how to solve polynomials and linear factors.Can you help with the problem so i can understand.
Write each expression as a polynomial in standard form.
(x-3)^2(x-1)
Click here to see answer by richwmiller(9135)

Question 254283: Writing this function in factored form:
y=4x^3-49x
Click here to see answer by richwmiller(9135)

Question 254283: Writing this function in factored form:
y=4x^3-49x
Click here to see answer by nerdybill(6958)

Question 254392: how do you factor x^3-6x^2+3x-18
Click here to see answer by richwmiller(9135)

Question 254399: check my work??
the problem:
what is the product of (x^3+x^2+1)(x^2-x-5)
the answer:
x^5-6x^3+x^2-x-5
Click here to see answer by MathLover1(6632)

Question 254427: Find the least value of the polynomial p(x) = x^4 - 4x^3 + 6x^2 - 4x + 6.
Click here to see answer by Theo(3464)

Question 254427: Find the least value of the polynomial p(x) = x^4 - 4x^3 + 6x^2 - 4x + 6.
Click here to see answer by Alan3354(30993)

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