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

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Question 472093: A pilot flies 630 miles with a tail wind of 35 miles per hour. Against the wind, he flies only 455 miles in the same amount of time. Find the rate of the plane in still air.
Click here to see answer by jorel1380(2518)

Question 472117: A boater travels 16 miles per hour on the water on a still day. During one particular windy day, he finds that he travels 48 miles with the wind behind him in the same amount of time that he travels 16 miles in to the wind. Find the rate of the wind.
Click here to see answer by jorel1380(2518)

Question 472121: I am trying to add a rational expression with an unlike denominator.
Simplify the expression: 3/x + 2/x^2
I do not understand from my math book how to find the least common denominator in order to rewrite the fractions using the least common denominator.
So far I am at:
3/x + 2/x*x
I understand that the least common denominator contains the highest power of each factor that appears in either denominator. So does that mean that the least common denominator is x from both denominators giving you x^2?
If that is so, I come up with: 3x/x^2 + 2/x^2
If I combine these two I have (3x + 2)/x^2
Is this thinking process correct?
Click here to see answer by mananth(12270)

Question 472158: 3x^2+22x-16=0
Click here to see answer by jim_thompson5910(28593)

Question 472075: Which of the following describes the end behavior of the graph of the
function f(x) = 4x5 – x + 10 ? Explain.

A. Upward to the left and downward to the right(i think this is the correct answer)
B. Downward to the left and upward to the right
C. Upward to the left and upward to the right
D. Downward to the left and downward to the right

Click here to see answer by richard1234(5390)

Question 472212: A student is asked to solve b2 + x2 = a2 and gives the following solution.
b2 + x2 = a2
sqrt(b2 + x2) = sqrt(a2)
b + x = a
x = a − b
Find the multiple mistakes the student made and explain why they are incorrect
**sqrt = square root
Click here to see answer by richard1234(5390)

Question 472213: 7-sqrt(x2 − 3x)=sqrt((x2 − 3x) + 5)
Step 1: Assume that we can represent (x2-3x) by u.
Step 2: Rewrite the equation with u.
Step 3: Solve the reduced equation given in Step 2 and replace u with the expression given in Step 1.
Step 4: What are the solutions of the original equation?
**sqrt=square root
Click here to see answer by ccs2011(207)

Question 472207: Give the equation of the oblique asymptote, if any, of the function.

A.
B.
C.
D. no oblique asymptote

Click here to see answer by ccs2011(207)

Question 472207: Give the equation of the oblique asymptote, if any, of the function.

A.
B.
C.
D. no oblique asymptote

Click here to see answer by lwsshak3(6491)

Question 472101: Find all zeros of the function and write the polynomial as a product of linear factors.

a. f(x) = (x - 4)(x + 2)(x - 3)(x + 3)
b. f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)
c. f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)
d. f(x) = (x - i(sqrt8))(x + i(sqrt8))(x - 3)(x +3)

Click here to see answer by lwsshak3(6491)

Question 472235: factor out completely 6x^3y-15x^2y-9xy
Click here to see answer by MathLover1(6627)

Question 472466: I am in college prep math and had a question about multiplying and simplifying rational expressions. The problem I am stuck on is xsquared-25 over xsquared-3x-10 times or multiplied by x+2 over x
I factored the numerator and denominator then cancelled out similar factors
The answers I got were x+5 over x which I simplified to 5 by canceling out the x's
Click here to see answer by monika_p(71)

Question 472516: 64c^9 - 27y^6 Factor
Click here to see answer by jim_thompson5910(28593)

Question 472666: 9x-27/9x
Simplify by removing factors of 1?
Click here to see answer by jim_thompson5910(28593)

Question 472663: 2/6w+5
Find all numbers for which the rational expression is undefined?
Click here to see answer by algebrahouse.com(1079)

Question 472665: x^2-9/3-x
Simplify by removing factors of 1?
Click here to see answer by edjones(7569)

Question 472667: The speed of train A is 14mph slower than the speed of train B. Train A travels 190miles in the same time it takes train B to travel 260miles. What is the speed of each train?
Click here to see answer by edjones(7569)

Question 472674: To determine the number of deer in a game presurve, conservationists catch 697 deer and tags them. Later 408 deer are caught; 204 of them are tagged. How many deer in the presurve?
Click here to see answer by edjones(7569)

Question 472744: What is a fourth degree polynomial with integer coefficients that has the given zeros: 0,3,-2i.
Click here to see answer by stanbon(57307)

Question 472905: Identify the degree of each term of the polynomial and the degree of the polynomial
-6x^3+6x^2+9x+7
^means it is raising to that power.
Click here to see answer by stanbon(57307)

Question 472907: multiply
(c+1/4)(c+1/3)
those are suppose to be fractions
Click here to see answer by stanbon(57307)

Question 472910: factor
a^2+6a+9
^means it is raising to that power
Click here to see answer by Alan3354(30993)

Question 472912: rewrite the following expression with positive exponents
(24xy)^ -5/6
^means it is raising to the negative 5/6 power. 5?6 is suppose to be a fraction
Click here to see answer by Theo(3458)

Question 472793: The formula r=2√5L can be used to approximate the speed r, in miles per hour, of a car that's left skid marks length L, in feet. How far will a car skid at 20 mph?
Click here to see answer by ankor@dixie-net.com(15649)

Question 472973: Find a polynomial function of degree 3 with the given number as zeros?
-5, sqrt3,-sqrt3
Click here to see answer by robertb(4012)

Question 472974: Find the maximum number of x-intercepts and the maximum number of turning points that the graph of the function can have.
f(x) = – x2 + x4 – x6 + 3
Click here to see answer by robertb(4012)

Question 472882: How do I factor-
(m + 4)(a – 5) + (m + 4)(a + 3)
Click here to see answer by robertb(4012)

Question 473005: greatest common factor of 15x^3y^2z and 12x^2yz^2 ?

Click here to see answer by mananth(12270)

Question 473100: 9t -5 < 7t
Click here to see answer by Tatiana_Stebko(1326)

Question 473100: 9t -5 < 7t
Click here to see answer by MathLover1(6627)

Question 473143:

Quadratics: solvers

Practice!

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Please assist. I'm stumped..know making it harder than it is....--------------------------------------------------------------------------------
Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1.8x +9.871 where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
The shop should build ______ bicycles.

Click here to see answer by stanbon(57307)

Question 473175: solution to 3a + 6 < 21

Click here to see answer by stanbon(57307)

Question 473175: solution to 3a + 6 < 21

Click here to see answer by algebrahouse.com(1079)

Question 473351: If x + y = 12, xy = 27, then find the value of x³ + y³

Click here to see answer by Edwin McCravy(8908)

Question 473314: How do you divide this

Thank u
Click here to see answer by Edwin McCravy(8908)

Question 473540: factor the expression x^2 + 5x - 24
Click here to see answer by jim_thompson5910(28593)

Question 472489: find a polynomial function of degree 4 with -2 as a zero of multiplicity 1, 3 as a zero of multiplicity 2, and -1 as a zero of multiplicity 1
please show steps so i can learn. thanks!
Click here to see answer by richard1234(5390)

Question 472874: Explain in your own words how to evaluate a ploynominal for a givin value of a variable, demonstrate process with example.
Click here to see answer by richard1234(5390)

Question 473585: Factor completely
4c^2-9
^means it is raising to that power
Click here to see answer by richard1234(5390)

Question 473600: Evaluate the polynomial for x=4
2x^2-2x+5
^means it is raising to that power
Click here to see answer by jim_thompson5910(28593)

Question 473591: perform the indicated operations and simplify
x-1/x-5 - x+1/x+5 + x-45/x^2-25
^means it is raising to that power and these are all fractions so it is x-1 on top and x-5 on the bottom. The same goes with the other two
Click here to see answer by mananth(12270)

Question 473601: Add
(5v^4-4v^3+2v^2+13v-6)+(v^5+10v^3+8v^2-2v+4)+(-8v^4+v^2-9v-10)
^ means it is raising to that certain power.
Click here to see answer by ashleighb84(7)

Question 473587: solve
c^2+c-12=0
^means it is raising to that power
Click here to see answer by Alan3354(30993)

Question 473733: find the greatest common factor of 20a^3b, 16a^2, and 36ab^3
Click here to see answer by rfer(12657)

Question 473733: find the greatest common factor of 20a^3b, 16a^2, and 36ab^3
Click here to see answer by ewatrrr(10682)

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, 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