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

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Question 1105917: What is the least possible degree of a polynomial if it has 4 turning points?
Click here to see answer by math_helper(2461)

Question 1106024: What's the end behavior of 5x^3 - 3x^2 + x?
Click here to see answer by josgarithmetic(39613)

Question 1106025: The graph of a rational function has a local minimum at (7,0). The complex number 4 + 2i is ro of the function. What is the least possible degree of the function?

Click here to see answer by ikleyn(52754)

Question 1106173: In the vicinity of a bonfire the temperature T (in �C) at a distance of x meters from the center of the fire is given by
T(x) =
500,000
x2 + 400
.
At what range distances from the fire's center is the temperature less than 310�C? (Assume x is positive. Round your values to one decimal place. Enter your answer using interval notation.)

Click here to see answer by Boreal(15235)

Question 1106174: Find all values of x for which the graph of f lies above the graph of g. (Enter your answer using interval notation.)
f(x) = x^2; g(x) = 4x + 21
Click here to see answer by josgarithmetic(39613)

Question 1106271: Express this sentence as a formula: z varies directly with the square of s
Click here to see answer by josgarithmetic(39613)

Question 1106271: Express this sentence as a formula: z varies directly with the square of s
Click here to see answer by ikleyn(52754)

Question 1106371: Did the way my school factored this make sense or is there an easier way to solve this?
y^4 + y^2 - 6
Their solution:
When a problem looks slightly odd, we can make it appear more natural to us
by using substitution (a procedure needed for calculus). Let u=y^2. Factor the expression with u�s. Then, substitute the y^2 back in place of the u�s. If you can factor more, proceed. Otherwise, you are done.
1.(y^2-2)(y^2+3)
2. y^4+y^2-6
3. u^2+u-6
4. (u2-2)(u+3)
Click here to see answer by josgarithmetic(39613)

Question 1106536: The percent of carbohydrates by weight in grapes is 15%. The percent of carbohydrates in an orange is 7%. Danika consumed a total of 325 g of grapes and oranges. The percent of carbohydrates in the mixture she ate was 10%. How many grams of grapes did she eat? How many grams of oranges?
Click here to see answer by josgarithmetic(39613)

Question 1106600: solve the following:
1. 2x + 6 < 5 ( x - 3)
2. -2 (x - 3) > -3 (x + 2)
3. - (x + 5) < 2 (1 - x)
4. 1/4(x-3) < 1/3x
Click here to see answer by josgarithmetic(39613)

Question 1106601: A polynomial function has zeros -3 and 4. Which is one of the factors of the polynomial?
Click here to see answer by ikleyn(52754)

Question 1106676: The largest value of b for which x^2+bx+32 can be factored over the integers is.....?
Click here to see answer by Alan3354(69443)

Question 1106675: Subtracting the product of (3x-1) and (2x^2-4x+3) from the sum of
(2x^3-7x^2-6) and (x^2+6x-3) results in a polynomial of the form (ax^3+bx^2+cx+d). What is the value of b-2c?
Click here to see answer by josgarithmetic(39613)

Question 1106785: Please help me factor completely 2x^4 + 4x^3 - 8x^2 - 16x
I have a final tomorrow and I�m trying to review, not sure if I did it right.
Click here to see answer by ikleyn(52754)

Question 1106830: Verify the identity. Please help
cos 4u = cos^2 2u - sin^2 2u
Click here to see answer by greenestamps(13195)

Question 1106832: Verify the identity.
cotangent of x to the second power divided by quantity cosecant of x plus one equals
quantity one minus sine of x divided by sine of x

cot^2(x)/[csc(x)+1] = [1 - sin(x)]/sin(x)
Click here to see answer by Edwin McCravy(20054)

Question 1106848: If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -15x^5 - 7x^4 + 3
Click here to see answer by Boreal(15235)

Question 1106849: Solve for x. Round your answer to 2 decimal places.
A right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length eighteen units, is fifty degrees.
Click here to see answer by Boreal(15235)

Question 1106851: Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = three divided by square root of quantity three x plus four.
y= 3/sqrt(3x+4)
Click here to see answer by greenestamps(13195)

Question 1106850: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
5, -3, and -1 + 2i
Click here to see answer by greenestamps(13195)

Question 1106858: Perform the requested operation or operations.
f(x) = 7x + 6, g(x) = 4x^2
Find (f + g)(x).
Click here to see answer by josgarithmetic(39613)

Question 1106859: Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 6)^2
Click here to see answer by josgarithmetic(39613)

Question 1106859: Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 6)^2
Click here to see answer by JThomson(12)

Question 1106859: Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 6)^2
Click here to see answer by greenestamps(13195)

Question 1106817: when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided by (x-3), the remainder is 7. And also if p(x) is a cubic function in which x� is unity, q(x) is the quotient when divided by (x-2)(x-3) and p(1)=1. determine q(x) and p(x).
Click here to see answer by JThomson(12)

Question 1106856: Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
x - 2; 4x^2 - 3x + 22
Click here to see answer by ikleyn(52754)

Question 1106891: what is -8x^2-15+2 factor the quadratic expression completely

Click here to see answer by josgarithmetic(39613)

Question 1106926: Obtain the equation of the curve y=ax^2+bx+c,using the following conditions
(i) d�y/dx�=2
(ii) The curve is at minimum when x=-1/2
(iii) The curve passes through the point (-2,- 4).
Click here to see answer by Fombitz(32388)

Question 1106925: factorise completely 4y^3-3y-6
Click here to see answer by Alan3354(69443)

Question 1106933: Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
254�
Click here to see answer by abdulaleem(11)

Question 1106938: Perform the requested operation or operations.
f(x) = 7x + 6, g(x) = 4x^2
Find (f + g)(x).
Click here to see answer by Fombitz(32388)

Question 1106947: The stopping distance, d, of a particular car after the brakes are applied varies directly as the square of the rate, r. If the car is travelling 40 mph, it can stop in 80 feet. How many feet will it take the same car to stop when it is travelling 80 mph?
Click here to see answer by Boreal(15235)

Question 1106857: Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
254�
Click here to see answer by KMST(5328)

Question 1107103:
A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by h=-16t^2+48+4320.
What is the rocket's maximum height?
How long does it take for the rocket to reach its maximum height?
After it is fired, the rocket reaches the ground at t= sec.
Click here to see answer by Alan3354(69443)

Question 1107089: There are two triples of positive integers (a,b,c and d,e,f) such that and . Evaluate the expression |abc-def|.
Click here to see answer by ikleyn(52754)

Question 1107226: There�s a square which is 12y^4 inches on each side, express the area of the square as a monomial.
Click here to see answer by algebrahouse.com(1659)

Question 1107370: Form a polynomial whose zeros and degree are given.
Zeros: 88, multiplicity 1; negative 1−1, multiplicity 2; degree 3
Click here to see answer by ikleyn(52754)

Question 1107205: Find the polynomial that describes the area he has to mow minus the area of the shed
Dimensions of the yard are height 5x width 13x-4.
The dimensions of the shed are height 2x width 2x+4.
The polynomial in your final answer should only have two terms combine and simplify like terms

Click here to see answer by Alan3354(69443)

Question 1107401: The sum of two integers is 8 and the sum of their squares is 19 more than their product. Find the integers.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1107423: Solve for x:
2x^2-x=12+x
Click here to see answer by Alan3354(69443)

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