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

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Question 551510: Megan factored the expression 28x^2 + x - 15 as (4x-3)(7x+5). But when Jacob applied the FOIL principle and multiplied out (4x-3)(7x+5), he got 28x^2 - x - 15; thus, Megan’s solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.
Click here to see answer by jim_thompson5910(28476)

Question 551802: Simplify (3a^2b)(-3ab)^3
Click here to see answer by jim_thompson5910(28476)

Question 551467: Simplify: (2y)(-3y^4)^3
Click here to see answer by jim_thompson5910(28476)

Question 551803: Simplify (-g)^3(-g)^2
Click here to see answer by jim_thompson5910(28476)

Question 551803: Simplify (-g)^3(-g)^2
Click here to see answer by Alan3354(30965)

Question 551804: Simplify -(ab3)^3
Click here to see answer by deborabr(181)

Question 551804: Simplify -(ab3)^3
Click here to see answer by jim_thompson5910(28476)

Question 551804: Simplify -(ab3)^3
Click here to see answer by Alan3354(30965)

Question 552011: factoring polynomials
[Sum of cubes]: x^3 + y^3 = (x + y)(x^2 − xy + y^2)
[Difference of cubes]: x^3 - y^3 = (x-y)(x^2 + xy + y^2)
problem:
250x^4-54x
Click here to see answer by Earlsdon(6287)

Question 552022: Factor the following expression into a product of two binomials:
64x^2 - 64x + 16
Click here to see answer by stanbon(57223)

Question 552022: Factor the following expression into a product of two binomials:
64x^2 - 64x + 16
Click here to see answer by edjones(7569)

Question 552020: Use the “difference of squares” rule to factor the following expression:
9m^2 - 100n^4
Click here to see answer by stanbon(57223)

Question 552020: Use the “difference of squares” rule to factor the following expression:
9m^2 - 100n^4
Click here to see answer by Alan3354(30965)

Question 551887: Explain three rules for exponents Do not explain Exponent of 1 or 0).
Click here to see answer by richard1234(5390)

Question 552015: Factor out the greatest common factor from the expression
10x^2yz^3 – 6x^2y^2z – 4xy^3z^2
Click here to see answer by AnlytcPhil(1276)

Question 552057: 7-w/9-w = 2/w-9
Click here to see answer by Maths68(1474)

Question 552082: I need help solving this problem can some help me with this?
-5x^3+7x+10 when x = 3
Click here to see answer by rfer(12645)

Question 552019: Factor out the greatest common factor from the expression
16x^3y^2z^3 – 2x^2yz^3 + 14y^3z^4
Click here to see answer by rfer(12645)

Question 552067: Question #1
The expression is: u^2-12u+___
The challenge is to "Fill in the expression to make a perfect sqare"
Can you help me?
(the ^ is for the power)
Click here to see answer by neatmath(300)

Question 552110: -8x Is this a polynomial or not?
Click here to see answer by JBarnum(2044)

Question 552110: -8x Is this a polynomial or not?
Click here to see answer by mananth(12270)

Question 552162: Write each polynomial in standard form. Then classify it by degree and number of terms.
4x4 + 6x3 -2 - x4

Click here to see answer by jim_thompson5910(28476)

Question 552338: Solve by factoring:
4x2 − 12x + 9 = 0

Click here to see answer by Alan3354(30965)

Question 552308: I need help writing a polynomial:
Write a polynomial of the smallest degree with roots -8, 9, 10, and -11. Type your answer in standard form, with the equation equal to zero.
Thanks!
Click here to see answer by KMST(1865)

Question 552386: In solving the equation (x + 4)(x – 7) = -24, Eric stated that the solution would be
x + 4 = -24 => x = -28
or
(x – 7) = -24 => x = -17
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
Click here to see answer by richard1234(5390)

Question 552407: Essay question: Could you please show all work? Find difference.
(-7x^2+5x-9)-(2x^2+7x+5)
Click here to see answer by jim_thompson5910(28476)

Question 552399: Short answer. State the degree of the given polynomial 7x^5-4x^4+7x^2-6
Click here to see answer by jim_thompson5910(28476)

Question 552396: Essay question: Show all work. Suzie's flower shop estimates that supplies costs for one month will be given by the polynomial 5x^2-3x+1. She estimates that utilities cost for one month is given by x-9. Find and simplify an expression that would estimate Suzie's total costs for one month.
Click here to see answer by richard1234(5390)

Question 552448: List the coefficient of the given polynomial 6x^3-x^2+x+7
6,1,1
6,-1,1
3,2,1,
6,-1,1,7

Click here to see answer by kamallohia(18)

Question 552447: Essay question: Show all work. Suzie's flower shop estimates that supplies costs for one month will be given by the polynomial 5x^2-3x+1. She estimates that utilities cost for one month is given by x-9. Find and simplify an expression that would estimate Suzie's total costs for one month.
Please show work
Click here to see answer by Theo(3458)

Question 552444: Factor Completely
ax+2x+a+2
Click here to see answer by mananth(12270)

Question 552401: Short answer: Adding the following (-7.4x^2+1.8x-8.5) + (2x^2+6x+2.3)
Click here to see answer by Maths68(1474)

Question 552474: 1.
Is zero a solution of -2 < x < 5?

yes

no
Click here to see answer by mananth(12270)

Question 552467: Essay: List the terms, coefficient, and degree of the following polynomial 5x^3y^2+2xy-6y please show work
Click here to see answer by mananth(12270)

Question 552465: Short answer. State the degree of the following polynomial: 5x^3y^2+2xy-6y please show work
Click here to see answer by mananth(12270)

Question 407818: I am looking for some help with this math problem. Thank you.
A 5ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 1 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
Click here to see answer by lisapivaral(1)

Question 552527: 1. (4+2i) (1-5i)
a. Use foil to multiply the complex numbers. show work.
b. combine any like terms from step 1. show work.
Click here to see answer by stanbon(57223)

Question 552527: 1. (4+2i) (1-5i)
a. Use foil to multiply the complex numbers. show work.
b. combine any like terms from step 1. show work.
Click here to see answer by Alan3354(30965)

Question 552528: 1. (6-3i)/(2+i)
a. Multiply the numerator and the denominator by the conjugate. show work.
b. combine any like terms from step 1. show work
Click here to see answer by Alan3354(30965)

Question 552530: 1. If the highest power of any polynomial function is_______, the graph will rise to the left and rise to the right (even or odd; choose the term that correctly fills in the blank).
Click here to see answer by stanbon(57223)

Question 552531: 1. If the highest power of any polynomial function is_______, the graph will fall to the left and rise to the right (even > or odd; choose the term that correctly fills into the blank).
Click here to see answer by stanbon(57223)

Question 552542: 1. x^2+8x=20

a. Add (b/2)^2 to both sides of the equation.
b. Factor the left sides of the equation.

c. Take the square root of both sides of the equation from step 2.
d. simplify the radical and solve for x. show work.
Click here to see answer by Alan3354(30965)

Question 552538: 1. (6-3i)/(2+i)
a. Multiply the numerator and the denominator by the conjugate. show work.
b. combine any like terms from step 1. show work
Click here to see answer by Alan3354(30965)

Question 552552: Divide:

Click here to see answer by AnlytcPhil(1276)

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