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

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Question 149831: 1. Explain why a^2 + b^2 cannot be factored.
2. Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that was used that was not trial and error.
Click here to see answer by stanbon(57214)

Question 149844: Please keep me solve this problem:
2(x+2)^0
Click here to see answer by Alan3354(30955)

Question 149853: Pleas help me solve the follwing problem:
(2x^2) (3x^0) (x) (2x) = ?
Click here to see answer by nerdybill(6948)

Question 149852: Please help me solve the following problem:
2^-2 + 5^-1
Click here to see answer by nerdybill(6948)

Question 149850: Please help me with the following ptoblem:
4^-1 - 2^-1
Click here to see answer by nerdybill(6948)

Question 149854: a+4(4)=a+4(a)
Click here to see answer by adamchapman(301)

Question 149865: Please help me solve this equation
((2x-a)/(x+a))-((x+3a)/(a-x))=(a^2/(a^2-x^2))+3
possible answers:
x=-8a
x=-4a
x=4a
x=8a
Click here to see answer by nerdybill(6948)

Question 149869: need steps and answer
Factor
x^2- 6x + 8
Click here to see answer by nerdybill(6948)

Question 149875: Factor by grouping:
3cd – 6cy + 2xd – 4xy
which one of these is it?
1. (3c + 2x)(d + 2y)
2.(d – y)(3c + 4x)
3. (3c + 2x)(d – 2y)
4.prime

Click here to see answer by nerdybill(6948)

Question 149876: Factor by grouping:
3cd – 6cy + 2xd – 4xy
which one of these is it?
1. (3c + 2x)(d + 2y)
2.(d – y)(3c + 4x)
3. (3c + 2x)(d – 2y)
4.prime

Click here to see answer by nerdybill(6948)

Question 149874: answer
18y^2-6
Click here to see answer by nerdybill(6948)

Question 149873: answer
18y^2-6
Click here to see answer by nerdybill(6948)

Question 149879: Factor:
x^2 + 13x + 42
What is one of the factors?
(x + 6) ,
(x – 7) ,
(x – 6) or
prime

Click here to see answer by nerdybill(6948)

Question 149939: Please help me solve the following polynominal division problem:
(2x^4-x^3-5x^2+x+7)/(x+1)
Click here to see answer by stanbon(57214)

Question 149940: (2x^6-13x^5+75x^3+2x^2-50)/(x-5)
Click here to see answer by jim_thompson5910(28476)

Question 149941: (4x^6+20x^5-24x^4-3x^2-13x+30/(x+6)
Click here to see answer by jim_thompson5910(28476)

Question 150029: f(x)=x^3+6x^2-25x+18
Find all the zeros of the given polynomial.
can anyone help me solve this, I am new to this type of question.
Jessica
Click here to see answer by Fombitz(13828)

Question 150030: can anyone help me solve for the quotient and remainder when
3x^3-12x^2-6x-20 is divided by x-5
Thank you!
Click here to see answer by stanbon(57214)

Question 150074: 4(x-2)=0 how do u work this problem out

Click here to see answer by Alan3354(30955)

Question 150101: Time to swing. The period T (time in seconds for one complete cycle) of a simple pendulum is related to the length L (in feet) of the pendulum by the formula 8T² = л²L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing?
Click here to see answer by nerdybill(6948)

Question 150140: I need help with this problem im not sure on how to solve this given its story problem setting, any help is appreciated.
If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples?
Click here to see answer by scott8148(6628)

Question 150179: solve the following:
24g^2-40g=32
Click here to see answer by stanbon(57214)

Question 150231: Can you help me solve this problem?
Add.
(3r^4-2r^3+2r^2+10r-4)+(r^5+9r^3+5r^2-2r-2)+(-6r^4+r^2-6r-9)
I would really appreciate an explanation on how to solve this problem. Thank you so much for your help once again.
Click here to see answer by jim_thompson5910(28476)

Question 150260: If A varies directly with the square of the length L and inversely with the parameter p, write an equation that expresses this relationship.
Click here to see answer by jojo14344(1512)

Question 150221: I am not quite sure the name of this kind of problem because I am still new at this, but if someone could help me I would really appreciate it. This is the problem. It states:
Multiply (7x+4)(7x^2+5x+4)
I get confused when it comes down to the steps and I would really appreciate the help. Thank you so much.
Click here to see answer by Fombitz(13828)

Question 150392: how do you simplify:
(5x^3-3x^2-6) (2x^3-6x^2)

i really need your help because im not sure if i can combine the different bases or powers. im really confused because i thought you could but a friend said that i couldnt so i dont know.
Click here to see answer by jim_thompson5910(28476)

Question 150375: 1. Consider the polynomial f(x)= x^3 + 6x^2 –9x-14
Find all of the zeros of the given polynomial. Test all possibilities.

2. If y varies inversely as x and y = 0.6 when x = 10, find y when x = 12.

Click here to see answer by stanbon(57214)

Question 150374: 1. Marika is a salesperson who must decide between two monthly income options:
Option 1: Salary of $1412 per month, plus 10% of monthly sales
or Option 1: Salary of $2000 per month, plus 6% of monthly sales
What must the monthly sales amount be so that Option 1 is a better choice for Marika than Option 2?
Show a correct inequality and solve it.

2. Solve (x + 5)(x – 4)(x – 7) <= 0 and write the solution set in interval notation. Show all work

Click here to see answer by stanbon(57214)

Question 150411: Please help me solve this problem!
Let f (x) = 7/5-x
A. State the domain
B. State the vertical asymptote(s)
C. State the horizontal asymptote
d. Find the inverse function of f.
Click here to see answer by jim_thompson5910(28476)

Question 150429: Please help me with this algebra problem. It states:
If a probasketball plaer has a vertical leap of about 25 inches, what is his hang time? Use the hang-time function V=48T^2.
Please help solve. Thanks.
Click here to see answer by nerdybill(6948)

Question 150428: Can anyone please help me with this problem?
Simplify by removing faqactors of 1. The simplified form is

p^2-1 /(divided by) (p+1)^2
Sorry I did not know how to put the division sign in. Please help me if possible.
Click here to see answer by nerdybill(6948)

Question 150433: Please help solve.
If the sides of a square are lengthened by 7cm, the area becomes 121 cm^2. Find the length of a side of the original square. The length of a side of the original square is ___________cm.
Click here to see answer by jojo14344(1512)

Question 150431: Please help.
Solve for x. 4x(x-2)-5x(x-1)=2
x=
Please help me solve ths problem as soon as possible. Thank you very much.

Click here to see answer by jojo14344(1512)

Question 150432: Help Solve please. I am so confused!!
Multiply.[a + 1/5][a+1/4]
Thank you for your help.
Click here to see answer by jojo14344(1512)

Question 150430: Please help me with this problem. I do not know how to do the radical sign on my keyboard. But the problem states:
Multiply
(2 radical sign 3 - 6radical sign 7)(4 radical sign 3 + 12 radical sign 7)
I hope that someone can understand and help me with this problem. Thank you for your assistance.
Click here to see answer by stanbon(57214)

Question 150450: Simplify the polynomial

15^2 + 4x- 5x + 5x^2+ 9
Click here to see answer by jim_thompson5910(28476)

Question 150461: How does the value of the variable a affect the direction of the parabola opens?
I think this is the right answer but I'm not sure.
If the value is negative, it opens downward.
If the value is positive, it opens upward.
Or does it have no affect?
________________________________________________________________________________
Also...
How does the value of variable a affect the width of the parabola?
I think this is the answer but I don't know.
The value does not affect the width of the parabola
Or is it
The closer or further to the 0 the more wider/narrow it gets?
Click here to see answer by Fombitz(13828)

Question 150465: I haven't been able to figure out the answer. How do I solve the following problem:
x^2 + 3x + 1
Click here to see answer by jim_thompson5910(28476)

Question 150472: (-27x^9)^⅓
Click here to see answer by edjones(7569)

Question 150259: Determine solution set x+5/x-4>3x+2/2x+1
Click here to see answer by edjones(7569)

Question 150482: Factor-
5x^2y^62^4 - 15x^4y^5z^3 + 2-x^3y^5z^2
Could you please help me do this problem. Once i can understand how it was done, than i can do the rest of my problems. Thank you
Click here to see answer by MathTutorer(13)

Question 150527: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree: 18; Zeros: 3 and 1+i. I know that the other zero has to be 1-i, however, I seem to have misplaced my notes from class and my textbook is not offering much help. Any assistance would be greatly appreciated. Thanks.
Click here to see answer by jim_thompson5910(28476)

Question 150602: Please help me find x.
-12x^3 + 52x^2 + 54x + 12 = 0
I don't know where to go from here? Please show work so I know how to do problems like this from now on, Thanks!
My work that I think is wrong...
-12(x^3 - (13/3)x^2 - (27/6)x - 1) = 0
Thanks again for your help!
Click here to see answer by stanbon(57214)

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