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

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

Question 1023618: Please show work
Donut Delights, Inc. has determined that when x donuts are made daily, the profit P, in dollars, is given by
P(x) = �0.002 x2 + 4.1x � 1200
(a) What is the company�s profit if 600 donuts are made daily?
(b) How many donuts should be made daily in order to maximize the company�s profit? Show work.
Click here to see answer by Emilym1234(10)

Question 1023684: Find a polynomial equation with integral coefficients that has the given numbers as solutions and the indicated degree.
2, -4/5, 1/2 ; degree 3
Please help me solve. Thank you.
Click here to see answer by Alan3354(69443)

Question 1023686: Use the rational root theorem and the factor theorem to help solve the equation.
A polynomial equation of degree n has n solutions, and any solution of multiplicity p is counted p times.
x^3 − 5x^2 − 13x − 7 = 0

Please help me solve. Thank you
Click here to see answer by MathLover1(20849)

Question 1023685: Use synthetic division to show that g(x) is a factor of f(x), and complete the factorization of f(x).
g(x) = x − 3, f(x) = x^3 − 5x^2 − 29x + 105
Please help me solve. Thank you

Click here to see answer by MathLover1(20849)

Question 1023621: Please help and show all work. Thanks

Real Zeros of Polynomials
1. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=−2. It goes through the point (5,14).
Find a formula for P(x).
P(x)=

2. The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and root of multiplicity 1 at x=-1. The y-intercept is y=-12.5.
Find a formula for P(x).
P(x)=
Click here to see answer by KMST(5328)

Question 1023641: Consider the polynomial P(x), shown in both standard form and factored form.
P(x)=(1/5)x^4 −(3/5)x^3 −3x^2 +(19/5)x+6=1(x+3)(x+1)(x−2)(x−5)
a. State the y-intercept.
b. Please graph p(x)
Click here to see answer by Fombitz(32388)

Question 1023738: Hello Tutors,
Please help me solve this rational expression word problem.
When water is turned on and passes through a small hose, your pool can be filled in 8 hours. When the water is turned on at two spigots and passes through both the small and large hose, the pool can be filled in 4 hours. How long would it take to fill the pool using only the large hose?

Click here to see answer by josgarithmetic(39613)

Question 1023361: find all zeros and actual zeros of the given polynomial. then rewrite the polynomial in factored form.
f(x)=9x^4-3x^3-84x^2+24x+96
Click here to see answer by Fombitz(32388)

Question 1023753: Simplify the expression shown. (12x/5)/(6x/7) PLEASE HELP

Click here to see answer by Alan3354(69443)

Question 1023750: Solve the proportion: x/(x+3) = (x-2)/x ... Please help!
Click here to see answer by addingup(3677)

Question 1023842: Please find the general solution to by variation of parameters.

Click here to see answer by robertb(5830)

Question 1023872: My math book and the algebra app always leave problems unfinished. They say [(a^2-b^2)/(c+d)/(a-b)/(c^2-d^2)]=[(a+b)(c-d)]/(1). I think the answer is (ac-ad+bc-bd). Can you explain why everything leaves the problem unfinished?
Click here to see answer by FrankM(1040)

Question 1023877: Mel has some coins in her purse consisting of 1 peso, 5 peso and 10 peso coins. She has three more 5 peso coins than 10 peso coins. The number of her 1 peso coins is twice the number of her 5 peso coins. Which polynomial gives Mel's total amount of money if 'x' is the number of 10 peso coins?
choices given:
a. 4x+9
b. 15x+25
c. 16x+18
d. 17x+21
And please provide an explanation so I may understand my flaws with this problem.
Click here to see answer by Alan3354(69443)

Question 1022713: Write a binomial and a trinomial involving a single variable. Then find their product. Thanks for the help!
Click here to see answer by fractalier(6550)

Question 1023951: A polynomial function P and its graph are given.
P(x) = 2x^4 − 9x^3 + 9x^2 + x − 3

From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
x=
Click here to see answer by stanbon(75887)

Question 1023981: Use f(x) = 4x − 2 and g(x) = 5 − x^2 to evaluate the expression.
(a) (f ○ g)(−2)=

(b) (g ○ f)(−2)=

Click here to see answer by stanbon(75887)

Question 1024079: 65x2y and 52xy

Click here to see answer by fractalier(6550)

Question 1024178: factor the polynomial completely
9a^2c-36b^2c

Click here to see answer by stanbon(75887)

Question 1024521: What is the discriminant D of the equation? a^2 � 2a + 5 = 0 D=_______
Click here to see answer by Fombitz(32388)

Question 1024526: Use the discriminant to determine the number and type of solutions the equation has? x^2 + 8x + 12 = 0 A.no real solution B.one real solution C. two rational solutions D. two irrational solutions
Click here to see answer by Fombitz(32388)

Question 1024525: How many and what type of solutions does the equation have? 5y^2 = 18y � 4 A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions
Click here to see answer by rothauserc(4718)

Question 1024527: What is the discriminant D of the equation? 6y^2 + 2 = �7y
D = _________
Click here to see answer by Alan3354(69443)

Question 1024523: How many and what type of solutions does the equation have? �4x^2 � 2 = 10x A. no real solutions B. one real solution C. two rational solutions D. two irrational solutions
Click here to see answer by fractalier(6550)

Question 1024579: simplify the following equation
(x+7y)^2
Click here to see answer by Alan3354(69443)

Question 1022998: Karl is putting a frame around a rectangular photograph. The photograph is 12 inches long and 10 inches wide, and the frame is the same width all the way around. What will be the area of the framed photograph?
Click here to see answer by Fombitz(32388)

Question 1024712: 16w-5+4 , if w= 4
Click here to see answer by rfer(16322)

Question 1024726: The graph of (x)=-(x+3)^2(x-5)^3 has x-intercepts at x=-3 and x=5.
At and immediately surrounding the point x=-3, the graph resembles the graph of what function?
Choose one.
A. y=x
B. y=x^2
C. y=x^3
Click here to see answer by MathLover1(20849)

Question 1024789: Is it a polynomial, states its degree?
f(x) = x^3-4/x^5
Click here to see answer by josgarithmetic(39613)

Question 1024834: This is a nesting fraction. I tried the question on two different sites
when my main site, which has taught me a lot, didn't make sense. The question is or problem is 2+2/x (numerator) 4-4/x (denominator) What is the correct answer please. (Its suppose to be reduced as much as possible for the answer.)
Click here to see answer by ikleyn(52750)

Question 1024826: Why do we even factor? What is the purpose of it? What do we use it for?
Click here to see answer by ikleyn(52750)

Question 1024843: Factor the polynomial below if possible:
-16+49h squared
Click here to see answer by ikleyn(52750)

Question 1024867: Which equation represents the area of a rectangle with a length of 3x and a width of y+4
Click here to see answer by ikleyn(52750)

Question 1024406: F(X) = X^3 - 343x^3 Find all the X-intercepts of each polynomial.
Click here to see answer by Fombitz(32388)

Question 1024939: Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of it's zeros.
1+i, 2
So f(x)= ?
Click here to see answer by Fombitz(32388)

Question 1024938: Find a polynomial function of degree 3 with real coefficients that has the given zeros.
-1,2,-9
The polynomial function is f(x)= x^2+(answer?)x^2-11x-18
Click here to see answer by Fombitz(32388)

Question 1024996: I need help solving this problem completely. I need step-by-step instructions. Please include how long it take to fill the pool using only the large hose.
When water is turned on and passes through a small hose, your pool can be filled in 8 hours. When the water is turned on at two spigots and passes through both the small and large hose, the pool can be filled in 4 hours. How long would it take to fill the pool using only the large hose?

Click here to see answer by josgarithmetic(39613)

Question 1025070: rational between -1\7 and -1\8

Click here to see answer by Fombitz(32388)

Question 1024985: suppose the area of a rectangle is 4x^2-4x+1 and the length is 2x-1. What is the width? whats true about the sides of the rectangle.
Click here to see answer by Fombitz(32388)

Question 1024937: Given that the polynomial function has the given zeros, find the other zeros.
f(x)=x^3-11x^2+55x-125;5
The other zeros are?
I can not figure out this problem. Thanks:)
Click here to see answer by Fombitz(32388)

Question 1025165: how do you find the product of 20x(3-2x)

Click here to see answer by Alan3354(69443)

Question 1025264: solve 8x�+12x�+6x+1-27y�
Click here to see answer by ikleyn(52750)

Question 1024975: Determine a polynomial function of lowest degree with rational coefficients that has the following zeros: 1-square root of 5
Click here to see answer by Fombitz(32388)

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, 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