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

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Question 105284: okay, here is another one. I am not understanding the whole exponent thing.
Simplify each of the following expressions. Write your answers with positive exponents only.
(m^4)^-3/(m^-2)^4
The book shows two different examples according to different properties, how do I know which one to apply?? I am really confused with the properties overall.
Help!

Click here to see answer by checkley75(3666) About Me 

Question 105264: Find the following square.
(3a- 4b)^2

Click here to see answer by HyperBrain(694) About Me 

Question 105288: 1/x+1/(x+1)= 1/1.5
why can't i get this?

Click here to see answer by edjones(8007) About Me 

Question 105348: I was doing great until I ran into this one please help!
Find all positive values for k for which each of the following can be factored
x^2 + 5x + k
Thank you very much!

Click here to see answer by edjones(8007) About Me 

Question 105279: Hello,
I looked and count not find anything related to this one on your site. Can you please help me I am having a hard time with this one.
Perform the indicated divisions.
x^3 + 4x - 3 /x + 3
What do I do with the exponent? Does it factor with the other variables?
Help!

Click here to see answer by edjones(8007) About Me 

Question 105200: b-2 /b^2-4 over
b^2+b/b+1
Divide and simplify Factor if necessary

Click here to see answer by elima(1433) About Me 

Question 105272: Find the greatest common factor for each of the following sets of terms.

9b^3, 6b^5, 12b^4

Click here to see answer by elima(1433) About Me 

Question 105574: Tutor please help me with this question
8(1+1/2)^2 +22(1+1/t)+15=0
Thank you!

Click here to see answer by bucky(2189) About Me 

Question 105577: I have lawn beds 20 inches wide, by turning up the edges to form right angles. Find the depth that will maximize its cross-sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 105596: Factoring when either square is a sqaure of a polynomial.
A^2-(b+c)^2

Click here to see answer by MathLover1(20849) About Me 

Question 105600: find the additive inverse of this polynomonal" 6x^2+x"
Click here to see answer by MathLover1(20849) About Me 

Question 105764: find the polynomial expression for the factors
(x+2)(x-3)(x+5)(x+6)

Click here to see answer by manoj_mcse2k3(1) About Me 

Question 105682: how do you find the square of a binomail?

Click here to see answer by HyperBrain(694) About Me 

Question 105707: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)

Click here to see answer by HyperBrain(694) About Me 

Question 105763: I have a hard time with word problems. Could you please help me get started on this? I don't want the answer, just a good jumpstart on how to begin.
The volume of the box is represented by (x^2+5x+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
It also has the equation x+2 next to a picture of the box.
I think that the formula for area is:
A=2LW+2LH+2LW
A=Area
L=length
W=width
H=height
I am really unsure on how to begin this. Again, if you can get me started in the right direction, I would really appreciate the help.

Click here to see answer by bucky(2189) About Me 

Question 105706: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)

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

Question 105796: I need help. It's been a while and I need to be refreshed. I know the answer is 5x + 3 .... but I don't know how to get there!
Problem: (x^2+3x-2)-(x^2-2x-5)=

Click here to see answer by tutorcecilia(2152) About Me 

Question 105799: what are the rational zeros and other zeros
What are the linear factors
f(x)=3x4-4x3+x2+6x-2

Click here to see answer by stanbon(75887) About Me 

Question 105829: f(x)=32x^3-52x^2+17x+3 who do we list the possible rational zeros of f and can it be discarded and are there more than one zero's?
Click here to see answer by Fombitz(32388) About Me 

Question 105421: Hello everyone,
The question: Find the inverse of the function f(x) = +sqrt+%28x%5E2+%2B+%281%2Fx%5E2%29%29+
I am having trouble isolating the y for the inverse function. I would greatly appreciate any help. My work is shown below.
Thank you very much!
---
My work :
f(x) = +sqrt+%28x%5E2+%2B+%281%2Fx%5E2%29%29+
y = +sqrt+%28x%5E2+%2B+%281%2Fx%5E2%29%29+
x = +sqrt+%28y%5E2+%2B+%281%2Fy%5E2%29%29+
= +sqrt+%28%28y%5E4+%2B+1%29%2Fy%29+
+x%5E2+=+%28y%5E4+%2B+1%29%2Fy%5E2+
+x%5E2y%5E2+=+y%5E4+%2B+1+
+x%5E2y%5E2+-+y%5E4+=+1+
+y%5E2%28x%5E2+-+y%5E2%29+=+1+

Click here to see answer by TP(29) About Me 

Question 105908: Give one of the factors of
8q^3+64u^3


Click here to see answer by HyperBrain(694) About Me 

Question 105914: a lab is testing two high-speed trains. One train travels 40 km/h faster than the other train. While one travels 70km, the other travels 60 km. Find their speeds.
Please break it down.. thanks

Click here to see answer by HyperBrain(694) About Me 

Question 105917: Can someone please help me to factor this Polynominal? 16a^4 - 625b^4
Thank You Very Much!

Click here to see answer by HyperBrain(694) About Me 

Question 105916: Could not figure out how to put this into the solvers? Can someone please factor the following by grouping?7x^2 + 7xy + 4x + 4y????
Here is how I thought I was supposed to do this but I am not getting the right answer.
Combine like terms:
7x^2 + 4x = 11x^2
7xy + 4x+4y = 15xy
15xy + 11x^2
That is as far as I got. Am I even close? Please help? Thank You!

Click here to see answer by edjones(8007) About Me 
Question 105916: Could not figure out how to put this into the solvers? Can someone please factor the following by grouping?7x^2 + 7xy + 4x + 4y????
Here is how I thought I was supposed to do this but I am not getting the right answer.
Combine like terms:
7x^2 + 4x = 11x^2
7xy + 4x+4y = 15xy
15xy + 11x^2
That is as far as I got. Am I even close? Please help? Thank You!

Click here to see answer by Earlsdon(6294) About Me 

Question 105994: We were asked to perform the function indicated and simplify the answer.
(2x^2-5y)^2. My answer was 4x^4-20x^2y+25y. If it is correct am I able to simplify it further? Thank you in advance.

Click here to see answer by edjones(8007) About Me 

Question 106003: how can i factor this one?please help me...
12x^4+17x^2+6

Click here to see answer by edjones(8007) About Me 

Question 105945: I need to find the coordinates (x,y) of the point on the graph of y=-x+4 that is closest to the origin.I already found the point that minimize the square but then I don't know what to do.
Thanks for you help
eska

Click here to see answer by alvinjohnburgos(11) About Me 

Question 106000: hi....i really need ur help....i solved this problem but don't know if i get it correctly....thanks...

factor:
x^4 - 3x^2 + 1

Click here to see answer by HyperBrain(694) About Me 

Question 106036: Answer should be written in scientific notation:
2.6 x 10^-3 divided by 2.0x 10^2

Click here to see answer by Fombitz(32388) About Me 

Question 106019: The problem is= Determine all zeros for each polynomial function.
P(X)= x3-4x2+x
All I had was below
x2(X-4)(x+1)
one answer which is 0, but then I determined my factoring was incorrect and I feel like the problem is missing something, should it have a zero on the end?
Please help.

Click here to see answer by MathLover1(20849) About Me 

Question 106091: Hello once more. The question for today is:
x^2/x-3 - 9/x-3
(these are dealing with adding and subtracting like rational expressions.)
I know this so far:
x^2/x-3 - 9/x-3 = x^2-9/x-3.
I am usure of what to do with the numerator x^2-9.
I know that I cannot factor and simplify x^2-9 because there are no common factors between.
I think I should leave the final answer (because they just want us to write it in the simplest form as:
x^2-9/x-3.
Am I even close, or way off base?
I know that

Click here to see answer by stanbon(75887) About Me 
Question 106091: Hello once more. The question for today is:
x^2/x-3 - 9/x-3
(these are dealing with adding and subtracting like rational expressions.)
I know this so far:
x^2/x-3 - 9/x-3 = x^2-9/x-3.
I am usure of what to do with the numerator x^2-9.
I know that I cannot factor and simplify x^2-9 because there are no common factors between.
I think I should leave the final answer (because they just want us to write it in the simplest form as:
x^2-9/x-3.
Am I even close, or way off base?
I know that

Click here to see answer by Fombitz(32388) About Me 

Question 106161: Hi Again,
Thanks for everyone helping me! I am stuck on this one! Here is the directions and problem: If you believe that a polynomial is not factorable, label it as prime. Show all stages of factoring separately (i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again.
Problem: Factor Completely x^3 – 2x^2 + 7x – 14

Click here to see answer by stanbon(75887) About Me 

Question 106185: x^2+2x>0
Click here to see answer by stanbon(75887) About Me 

Question 106201: The problem is as follows= Given that x=1+2i is a zero for the funtion g(x)=3x^3-2x^2+7x+20, determine the remaining zeros.
The only solutions I know are 1+2i and 1-2i but I am having trouble getting the rest. PlEASE HELP

Click here to see answer by Edwin McCravy(20054) About Me 

Question 106208: Factor Completley
8x^2-200y^2

Click here to see answer by Edwin McCravy(20054) About Me 

Question 106206: How do you factor this completely and does it have a GCF?
x^10y^3-4x^9y^-21x^8y

Click here to see answer by Edwin McCravy(20054) About Me 

Question 106263: Factor completely:
x^10y^3 – 4x^9y^2 – 21x^8y
If you believe that a polynomial is not factorable, label it as prime. Show all stages of factoring separately (i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).
I am stuck on this one. Thanks in advance!

Click here to see answer by stanbon(75887) About Me 

Question 106311: indentify the vertex of the parabola y= x^2-2
Click here to see answer by Fombitz(32388) About Me 

Question 106371: Question 54. This is dealing with adding/subtracting rational expressions
(the below are supposed to be fractions, but I didn't know how to write them in here so you'd understand. Sorry if it doesn't come across pretty)

2 - 3
___ ___
5w+10 2w-4



This is what I have so far, but I am a bit confused.
I know that I need to find the LCD. Because of the numerators the way they are, I know that they are:
5w+10 which can be factored to 5(w+2)
2w-4 which can be factored to 2(w-2)
So, still they don't match as they have in other equations.
2*2(w-2) - 3*5(w+2)
___________ __________
5(w+2)*2(w-2) 2(w-2)*5(w+2) Not sure if I did that right
This then becomes:
4(w-2) - 15(w+2)
_________ __________
5(w+2)*2(w-2) 2(w-2)*5(w+2)
I am going to stop there, because I have a horrible feeling that I am way off track. Can you please help?

Click here to see answer by stanbon(75887) About Me 
Question 106371: Question 54. This is dealing with adding/subtracting rational expressions
(the below are supposed to be fractions, but I didn't know how to write them in here so you'd understand. Sorry if it doesn't come across pretty)

2 - 3
___ ___
5w+10 2w-4



This is what I have so far, but I am a bit confused.
I know that I need to find the LCD. Because of the numerators the way they are, I know that they are:
5w+10 which can be factored to 5(w+2)
2w-4 which can be factored to 2(w-2)
So, still they don't match as they have in other equations.
2*2(w-2) - 3*5(w+2)
___________ __________
5(w+2)*2(w-2) 2(w-2)*5(w+2) Not sure if I did that right
This then becomes:
4(w-2) - 15(w+2)
_________ __________
5(w+2)*2(w-2) 2(w-2)*5(w+2)
I am going to stop there, because I have a horrible feeling that I am way off track. Can you please help?

Click here to see answer by solver91311(24713) About Me 

Question 106487: product for
(3y^2+1)(3y^2-1)

Click here to see answer by MathLover1(20849) About Me 

Question 106490: You have a lot you believe to be 157' x 157'. After lot is surveyed you discover that one side is 2' shorter and the other side is 2' longer. How much less area do you have than originally believed?
Click here to see answer by stanbon(75887) About Me 

Question 106496: -4^0-8^0 Simplify expression.
My answer is -1-1=-2. Is this the correct answer?

Click here to see answer by scott8148(6628) About Me 

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, 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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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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, 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