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

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

Question 538071: (x+5)(x-3)=20
Click here to see answer by mananth(16946)

Question 538218: 4n^2-49
Click here to see answer by Alan3354(69443)

Question 538327: Choose the best response to describe the polynomial: 5x^4 + 8x^3 � 5x + 3

It is a trinomial.
It has a leading coefficient of 5.
It is of degree 5.
It is quadratic.

Click here to see answer by KMST(5328)

Question 538464: Find the LCM of 7(x-2)and 14(x-2). Please tell me if my solution to this is correct and if not why?
My solution: 7(x-2)

Click here to see answer by jim_thompson5910(35256)

Question 538509: Simplify by removing factors of 1; y^2-4y+4/y^2+4y-12
The answer I came up with is y+2/y-6, is this correct and if not what did I do wrong. Thanks!
Click here to see answer by MathTherapy(10549)

Question 538594: How to find rational roots of:
x^3 + 5x^2 - x - 5
I want to know what's the method.
Thank you
Click here to see answer by KMST(5328)

Question 538829: what are the solutions?
(r/4)-(4/r)=0
Click here to see answer by oberobic(2304)

Question 538816: 9x2-30x+25 factored fully
Click here to see answer by rfer(16322)

Question 539281: Find the x-intercepts and the vertex of the graph of
the function. Then sketch the graph of the function.
y = (x - 4)(x + 2)
y = (x - 2)(x - 6)
any help with this would be greatly appreciated, thanks.
Click here to see answer by Alan3354(69443)

Question 539493: THE factor polynomial problem is 15x2−84x−36
I know the answer to the polynomial is 3(5x+2)(x−6)but i dont understand how you get from
3(5x2−28x−12)to 3(5x+2)(x−6)<----the answer
can you please show me how you get it STEP BY STEP

Click here to see answer by jim_thompson5910(35256)

Question 539456: Patients with acute serious infections such as Salmonella Typhi or gram negative bacteria causing meningitis can be treated with regular doses of Chloramphenicol. A patient weighing 150 pounds requires a dose of 850 milligrams, while a patient weighing 300 pounds requires a dose of 1700 milligrams.
Lab experiments indicated that the concentration level C in milligrams per milliliter of the medication in the above patient�s bloodstream is a function of the amount of time t, in hours, since the medication is given by the quadratic equation: C (t)=83.3t^2 + 583.1t-170.4. For a drug to have a beneficial effect, its concentration in the bloodstream must exceed a certain value, called the minimum therapeutic level. The minimum therapeutic level of Chloramphenicol is 125 mg/ml.
Background-your patient
Weight: 240 lbs
Doctors orders:
The doctor wishes to use a 10% solution of Chloramphenicol, administered through an intravenous injection. The hospital only carries 5% and 20% solutions of the required medication.
1. Determine a linear function for determining the dosage needed for a patient based on the patients� weight in pounds.
2. Interpret the slope of this linear function
3. The dosage in milligrams, of Chloramphenicol needed for your patient
I did a ratio based on the information above and got X= 1360mgs
So for someone who weighs 240 lbs a dose of 1360mgs is needed.
4. Graph the function
6. Determine the amounts of each type of solution required to prepare 1000 ml of the 10% solution
7. Determine the dosage in milliliters rounded to 2 decimal places, of the 10% solution needed for your patient. Recall that medications are expressed as percent solution where the percent solution indicates how many grams of the active ingredient are dissolved in 100 milliliters of diluting elements (usually water or saline)
8. Determine how long after the IV injection it takes for the medication to start working

Click here to see answer by KMST(5328)

Question 539834: Essay: Show all work. The area of a rectangular swimming pool is given by 3x2+7x+4ft2. One side length of the pool is given by 3x + 4 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer.
Click here to see answer by mananth(16946)

Question 365305: The stadium vending company finds that sales of hot dogs average 31,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price per hot dog should be vending company charge to realize the maximum revenue? What is the maximum revenue?
Click here to see answer by karma333(1)

Question 540314: 89=4x+5

Click here to see answer by jim_thompson5910(35256)

Question 540326: 14x+20=22x-12
Click here to see answer by jim_thompson5910(35256)

Question 540326: 14x+20=22x-12
Click here to see answer by rfer(16322)

Question 540322: factoring polynominals 6x^7y^5+48x^5y^4+42xy
Click here to see answer by stanbon(75887)

Question 540548: 3x^2-5x-8=0
Click here to see answer by jim_thompson5910(35256)

Question 540593: I need help understanding Monomials/Polynomials/ and Factoring.
For example,
"If the length of a rectangle is 3x-2 and the width is 3x-1, what expression will represent the area of a rectangle."
If a rectangle has a width of 3x-y & length of 5x^2+y^3, what is the area?
[Factoring the Polynomials]
2x^2-8x^4
6x^2+7x-10
Please help ! Thank you
Click here to see answer by stanbon(75887)

Question 540567: how can you explain the concept of rational expressions in a easier form to someone who doesnt understand?
Click here to see answer by richard1234(7193)

Question 540634: Which are real zeros of this function? f(x)=x^3-6x^2-16x
Click here to see answer by scott8148(6628)

Question 540667: A^2-14a+49
Click here to see answer by mananth(16946)

Question 540700: (15x^2 z^4 -24xz^2) / -4x^2 z^4 please help me i need to simply this much as possible thank u ..... i would also recommend you to my friend at college. :)
Click here to see answer by mananth(16946)

Question 540641: I need some help with practice questions,
About monomials, polynomials, and factoring, simplifying.
[Simplifying polynomials]
(5x+4)(5x-4)
2x(x+5)+x(3-x)
5ab^2b(7ab^2+3a-4b)
(5m^2-2mp-6p^2)-2(-3m^2+5mp-p^2) (THIS ONE IS REALLY HARD)
&This is the only simplifying expression question I have trouble on:
(3x^2y^6)(-4x^2y^6)
If you could help, step by step.
thank you!
Click here to see answer by mananth(16946)

Question 540757: Why is the quotient of x^8 and x^2 = x^6 and not x^4
Click here to see answer by oberobic(2304)

Question 540791: Is this correct and what are the prime numbers 5,1 or 5,3?
Factor completely. If polynomial is a prime state this.
15t�+20t-75 factor GCF
5(3t�+4t-15)
5(3t�+9t-5t-15)
5(3t(t+3)-5(t+3)
5[(3t-5)(9t+3)] get rid of parentheses
5(3t-5)(t+3) no negative factors so the sign will not change
GCF=5
Prime = 5,3

Click here to see answer by fcabanski(1391)

Question 540908: Use ration exponents to write x^1/5*y^1/2*z^1/8 as a single radical expression
Click here to see answer by Theo(13342)

Question 540954: Factor Completely:

Click here to see answer by Theo(13342)

Question 540953: Factor completely:

Click here to see answer by Theo(13342)

Question 540985: Short Answer. Find the following quotient: x^2-4 / x+2

Click here to see answer by jim_thompson5910(35256)

Question 540990: I got myself lost some place and need help getting back on track.
I am factoring completly by grouping. Here are three problems:
1.

2.

3.

The final answer to number two is I am just having trouble getting thru the steps.
I understand you can substitute a single varable for a common part of the problem.
So in number2,

would be:

Would factor to:

Then putting back in (a^2+1)

Would further factor to:

or

That would be:

which is the answer in the back of the book. But how do you do it by factoring by grouping?

Click here to see answer by jim_thompson5910(35256)

Question 541032: x^3+7x^2-4x-28=0
Solve.
Click here to see answer by jim_thompson5910(35256)

Question 541033: Factor by completing the square.
x^2-12x-805
i can't remember how to do these.
Click here to see answer by richwmiller(17219)

Question 541034: 1-(a+b)^3
Factor the polynomial completely, write prime if the polynomial cannot be factored.
Click here to see answer by jim_thompson5910(35256)

Question 541067: "what is the answer for [5x(2a)�]�"

Click here to see answer by algebrahouse.com(1659)

Question 540971: essay: Show all work. find the quotient: 36a^2-b^2/6a-b
Click here to see answer by oberobic(2304)

Question 541125: Need a lesson on how to factor an expression with fractional exponets. Probably not searching the right thing on youtube.
I typed each twice because the formula plottting system is cutting off the top of the fractions on my screen.

Book gives the example:
3x^(3/2) - 9x^(1/2) + 6x^(-1/2)
= 3x^(-1/2) *(x^2-3x+2)
= 3x^(-1/2) (x-1)(x+2)

I am just not getting much from that example
I have a few problems in the book with the final answer:
x^(-3/2) + 2x^(-1/2) + x^(1/2)

The final answer is:
x^(-3/2) * (x+1)^2

Can you show me detailed steps?
Another problem is:
2x^(1/3)*(x-2)^(2/3) - 5x^(4/3)(x-2)^(-1/3)

The final answer is:
x^(1/3) *(x-2)^(-1/3)* (-3x-4)

Thanks in advace for your help!
Click here to see answer by stanbon(75887)

Question 540984: Essay: Show all work. A gardener wants to create a rectangular garden with length of 2x - 3y ft. and width of x + 4y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out, express in simplest correct mathematical form, and include units.

Click here to see answer by friesr(113)

Question 541149: Simplify the expression completely: (z/3)^2
Click here to see answer by friesr(113)

Question 541152: Essay: Show all work. The area of a rectangular swimming pool is given by3x^2+11x+6 ft^2 . One side length of the pool is given by 3x + 2 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer.
Click here to see answer by friesr(113)

Question 541154: Simplify the expression completely: (y^2/4)^3 please show me how to solve
Click here to see answer by friesr(113)

Question 541156: Essay: Show all work> Find the quotient:36a^2-b2 / 6a-b
Click here to see answer by lwsshak3(11628)

Question 541131: Factor:
a) x^2-y^2+3x+y+2
b) 2x^2-3y^2-5xy+x+11y-6
c) x^2(y-z)+y^2(z-x)+z^2(x-y)
I could only begin c) with expanding out the whole expression to:
x^2(y) - x^2(z) + y^2(z) - xy^2 - yz^2
I could not even attempt a) or b) and as mentioned above, I began c) with the expansion shown above.
Any assistance on these three problems would be greatly appreciated.
Click here to see answer by mananth(16946)

Question 541214: Simplify by removing factors of one
3n^2 +3n / 24n^2 +9n
Click here to see answer by stanbon(75887)

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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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, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105