Tutors Answer Your Questions about Polynomials-and-rational-expressions (FREE)
Question 1153810: I have no idea where to start. Ive been out of scholl for 20 yrs. HELP!!!
1. the revenue function of a fictional cable company can be modeled by the polynomial function:
R(t) = −0.037t4 + 1.414t3 − 19.777t2 + 118.696t − 205.332
where R represents the revenue in millions of dollars and t represents the year, with t = 1 corresponding to 2001. Using MS-Excel, create a graph of the Revenue Function and determine over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing?
Click here to see answer by MathLover1(20849)   |
Question 1153849: In questions 1 - 5, decide whether the given expression is a polynomial and tell why or why not.
1. 3x^2 - 5x + 2
AThis is not a polynomial because 5x is subtracted from 3x2.
BThis is a polynomial because 5 is in front of x.
CThis is not a polynomial because 3 is in front of x2.
DThis is a polynomial because it is the sum of monomials with whole-number exponents.
E This is not a polynomial because it contains x2.
F Not enough information.
2. 1/x^4 + 5x^2 - 4x + 1
AThis is a polynomial because it contains x2
BThis is not a polynomial because x4 is in the denominator.
CThis is not a polynomial because it contains x2
DThis is not a polynomial because there are too many exponents.
E This is a polynomial because the exponents can be divided evenly by two.
F Not enough information.
3. 4x^-3 + 3x^2 + 2x + 1
AThis is not a polynomial because there are too many exponents.
BThis is a polynomial because it contains x2
CThis is not a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x2
E This is not a polynomial because the terms are not written in the correct order.
F This is not a polynomial because x is raised to a negative power in the first term.
4. 7x^5 + 3x^4 - 2x^2 + 7
ANot enough information.
BThis is not a polynomial because 3 is in front of x2
CThis is a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x4
E This is a polynomial because it is the sum of monomials with whole-number exponents.
F This is not a polynomial because the exponents are not divisible by 2.
5. (√x) + 12
AThis is not a polynomial because the variable is underneath a square root sign.
BThis is not a polynomial because it does not contain x2
CThis is not a polynomial because the exponents are not divisible by 2.
DThis is a polynomial because it contains no negative exponents.
E This is a polynomial because there are no variables in the denominator.
F This is not a polynomial because the x has no positive coefficient.
Click here to see answer by greenestamps(13195)  |
Question 1153849: In questions 1 - 5, decide whether the given expression is a polynomial and tell why or why not.
1. 3x^2 - 5x + 2
AThis is not a polynomial because 5x is subtracted from 3x2.
BThis is a polynomial because 5 is in front of x.
CThis is not a polynomial because 3 is in front of x2.
DThis is a polynomial because it is the sum of monomials with whole-number exponents.
E This is not a polynomial because it contains x2.
F Not enough information.
2. 1/x^4 + 5x^2 - 4x + 1
AThis is a polynomial because it contains x2
BThis is not a polynomial because x4 is in the denominator.
CThis is not a polynomial because it contains x2
DThis is not a polynomial because there are too many exponents.
E This is a polynomial because the exponents can be divided evenly by two.
F Not enough information.
3. 4x^-3 + 3x^2 + 2x + 1
AThis is not a polynomial because there are too many exponents.
BThis is a polynomial because it contains x2
CThis is not a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x2
E This is not a polynomial because the terms are not written in the correct order.
F This is not a polynomial because x is raised to a negative power in the first term.
4. 7x^5 + 3x^4 - 2x^2 + 7
ANot enough information.
BThis is not a polynomial because 3 is in front of x2
CThis is a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x4
E This is a polynomial because it is the sum of monomials with whole-number exponents.
F This is not a polynomial because the exponents are not divisible by 2.
5. (√x) + 12
AThis is not a polynomial because the variable is underneath a square root sign.
BThis is not a polynomial because it does not contain x2
CThis is not a polynomial because the exponents are not divisible by 2.
DThis is a polynomial because it contains no negative exponents.
E This is a polynomial because there are no variables in the denominator.
F This is not a polynomial because the x has no positive coefficient.
Click here to see answer by MathLover1(20849) |
Question 1153869: Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no luck!
The function f(x)=x^3+3x^2+kx-4. The remainder when f(x) is divided by (x+2) is triple the remainder when f(x) is divided by (x-2). Determine the value of k.
At first I used (x-2), and let the value for x=2. Input 2 into the equation to find the value of K which i get -8. However when I try to do the division with both values to find the remainder to confirm my answer, everything goes haywire! Please help me :(
Click here to see answer by greenestamps(13195) |
Question 1153869: Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no luck!
The function f(x)=x^3+3x^2+kx-4. The remainder when f(x) is divided by (x+2) is triple the remainder when f(x) is divided by (x-2). Determine the value of k.
At first I used (x-2), and let the value for x=2. Input 2 into the equation to find the value of K which i get -8. However when I try to do the division with both values to find the remainder to confirm my answer, everything goes haywire! Please help me :(
Click here to see answer by ikleyn(52752)  |
Question 1153933: Hello,
I am working on a problem involving writing an expression for the area of the base.
The problem is: A cube shaped suitcase has a length of 3x+2 units. What is an expression for its area of the base?
How do you write an expression for the area of the base?
Thanks!
Click here to see answer by ramkikk66(644) |
Question 1153966: In problems 16-20, describe the mistakes, if any.
16. (-x + 4)(x + 2) solution: x^2 + 2x + 8
AThere should be a "+6" instead of a "+8."
BThere should be a "+6x" instead of a "+2x."
CThere should be a "-8" instead of a "+8"
DThere should be a negative with the x^2
E There should be a "-6" instead of a "+8"
F This solution is correct.
17. (3x^2 + 7)(9 - 8x) solution: 3x^2 - 56x + 63
AThere should be a "3x^3" term in the answer.
BThere should be a "-63" term in the answer instead of "+63".
CThere should be a "+56x" term in the answer instead of "-56x".
DThere should be a "-16" term in the answer.
E There should be a "-24x^3" term in the answer.
F This solution is correct.
18. 9x^2(6 - x)-8x(6 - x)/ x(6 - x)
solution: 1
ABoth of the x's in the 9x^2 term cannot be cancelled, so the answer should be 9x - 8.
BSince we have (6-x), we must multiply through by a negative, so the answer should be 17.
COnly one of the x's in the 9x^2 term can be cancelled, so the answer should be x.
DOnly one of the x's in the numerator can be cancelled, so the answer should be 1x.
E The expression cannot be simplified.
F This solution is correct.
19. [7x^4(x - 7) + 12x^4(x - 7)] / x^4(7- x)
Solution: 19
ATo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -5.
BTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -19.
CTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be +5.
D(x-7) will not cancel with (7 - x), so the answer should be [7(x - 7) + 12(x - 7)] / (7 - x)
E The expression cannot be simplified.
F This solution is correct.
Click here to see answer by MathLover1(20849) |
Question 1153966: In problems 16-20, describe the mistakes, if any.
16. (-x + 4)(x + 2) solution: x^2 + 2x + 8
AThere should be a "+6" instead of a "+8."
BThere should be a "+6x" instead of a "+2x."
CThere should be a "-8" instead of a "+8"
DThere should be a negative with the x^2
E There should be a "-6" instead of a "+8"
F This solution is correct.
17. (3x^2 + 7)(9 - 8x) solution: 3x^2 - 56x + 63
AThere should be a "3x^3" term in the answer.
BThere should be a "-63" term in the answer instead of "+63".
CThere should be a "+56x" term in the answer instead of "-56x".
DThere should be a "-16" term in the answer.
E There should be a "-24x^3" term in the answer.
F This solution is correct.
18. 9x^2(6 - x)-8x(6 - x)/ x(6 - x)
solution: 1
ABoth of the x's in the 9x^2 term cannot be cancelled, so the answer should be 9x - 8.
BSince we have (6-x), we must multiply through by a negative, so the answer should be 17.
COnly one of the x's in the 9x^2 term can be cancelled, so the answer should be x.
DOnly one of the x's in the numerator can be cancelled, so the answer should be 1x.
E The expression cannot be simplified.
F This solution is correct.
19. [7x^4(x - 7) + 12x^4(x - 7)] / x^4(7- x)
Solution: 19
ATo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -5.
BTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -19.
CTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be +5.
D(x-7) will not cancel with (7 - x), so the answer should be [7(x - 7) + 12(x - 7)] / (7 - x)
E The expression cannot be simplified.
F This solution is correct.
Click here to see answer by Edwin McCravy(20054)  |
Question 1153981: For problems 17 - 20, identify which of the methods from this lesson (GCF, grouping, difference of squares, or perfect squares) could be used to factor the polynomial.
17. x^2 + 2x + 1
AThis polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
BThis polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
CThis polynomial could be factored only by using the perfect squares method.
DThis polynomial could be factored only by using the difference of squares method.
E This polynomial could be factored by using grouping or the perfect squares methods.
F This polynomial cannot be factored by any of the methods used in this lesson.
18. 2x^3 + 4x^2 + 2x
AThis polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
BThis polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
CThis polynomial could be factored only by using the perfect squares method.
DThis polynomial could be factored by using grouping or the perfect squares methods.
E This polynomial could be factored only by using the difference of squares method.
F This polynomial cannot be factored by any of the methods used in this lesson.
19. x^2 - 169
AThis polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
BThis polynomial could be factored by using the difference of squares method or grouping.
CThis polynomial could be factored only by using the perfect squares method.
DThis polynomial could be factored by using grouping or the perfect squares methods.
E This polynomial could be factored only by using the difference of squares method.
F This polynomial cannot be factored by any of the methods used in this lesson.
20. x^2 + 5x - 7
AThis polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
BThis polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
CThis polynomial could be factored only by using the perfect squares method.
DThis polynomial could be factored by using grouping or the perfect squares methods.
E This polynomial could be factored only by using the difference of squares method.
F This polynomial cannot be factored by any of the methods used in this lesson.
Click here to see answer by MathLover1(20849) |
Question 1154000: Factor problems 9 - 12 by using the difference of squares method.
9. x^2 - 4
AThis polynomial cannot be factored by using the difference of squares method.
B(x - 2)(x - 2)
C(x - 2)(x - 1)
D(x - 2)(x + 2)
E (x - 1)(x - 4)
F (x + 2)(x + 2)
10. x^2 - 25
A(-x - 5)(x - 5)
BThis polynomial cannot be factored by using the difference of squares method.
C(-x + 5)(x + 5)
D(x - 5)(x + 5)
E (x + 5)(-x - 5)
F (x - 5)(x - 5)
11. 36x^4 - 4x^2
A(6x^2 - 2x)(6x^2 - 2x) = 4x^2(3x - 1)(3x - 1)
B(6x^2 + 2x)(6x^2 + 2x) = 2x^2(3x + 1)(2x + 1)
CThis polynomial cannot be factored by using the difference of squares method.
D(-6x^2 - 2x)(-6x^2 - 2x) = 4x^2(-3x - 1)(-3x - 1)
E (6x^2 - 2x)(6x^2 + 2x) = 4x^2(3x - 1)(3x + 1)
F (-6x^2 + 2x)(6x^2 - 2x) = 2x^2(-3x + 1)(3x - 1)
12. x^2 + 100
A(x + 10)(x - 10)
B(-x + 10)(x - 10)
C(x + 10)(x + 10)
DThis polynomial cannot be factored by using the difference of squares method.
E (x - 10)(x - 10)
F (-x + 10)(-x - 10)
Click here to see answer by josgarithmetic(39613) |
Question 1154232: Here is the multiple choice question:
Simplify ((−𝑥+1)/(x^2+3𝑥−4))*((8𝑥^2−4𝑥)/((𝑥−3)(𝑥+7))) and identify any restrictions on x
a. (3x^2+16x+16)/(x^2+3x-4), x<>-2/3
b. (3x^2-3x+4)/(-3x-2) x<>-3
c. (3x+4)/(3x+2), x<>-2/3
d. (3x+4)/(3x+2), x<>-2/3,-4,1
based on the restrictions on x, c must be the correct answer, but I can't figure out how to simplify to that expression. (Although I can't figure out why x <> -4, 3 or -7 as well)
Most obvious simplification is (-4x(2x-1))/((x+4)(x-3)(x+7)) but I don't know where to go from there to get any of the proposed solutions
Click here to see answer by MathLover1(20849) |
Question 1154813: A landscape architect is designing a rectangular garden in a local park. The garden will be 20 feet long and 15 feet wide. The architect wants to place a walkway with a uniform width all the way around the garden.
Click here to see answer by ikleyn(52752) |
Question 1154863: my first period algebra class has been working on polynomials for quite a while, i'm struggling to understand the topic, but have some sort of understanding of a few things inside the topic. so the problem i'm asking for help with looks like this;
given a polynomial has roots at -4 and 2i, find a third degree polynomial equation that would pass through these roots.
Click here to see answer by Theo(13342)  |
Question 1154871: You drop a ball from a height of 98 feet. At the same time, your friend throws a ball upward. The polynomials represent the heights (in feet) of the balls after t seconds. a. Before the balls reach the same height, write a polynomial that represents the distance between your ball and your friend’s ball after t seconds. The polynomial is . Question 2 b. The constant term is , indicating the distance between the two balls is feet when they begin. The coefficient of the linear term is , indicating the two balls become feet closer to each other each second.
Click here to see answer by Alan3354(69443)  |
Question 1155272: List all rational zeros that are possible according to the Rational Zero Theorem
The following function is given: f(X)=x3-5x2-4x+20
I am assuming that I look for the leading coefficient first
Then possible rational zeros Factors of the constant terms
Factors of the leading coefficient
I am going to assume that the constant term is 20.
The leading Coefficient would be 1, 5,-5,2-2,4.-4,20, -20
Click here to see answer by MathLover1(20849) |
Question 1155272: List all rational zeros that are possible according to the Rational Zero Theorem
The following function is given: f(X)=x3-5x2-4x+20
I am assuming that I look for the leading coefficient first
Then possible rational zeros Factors of the constant terms
Factors of the leading coefficient
I am going to assume that the constant term is 20.
The leading Coefficient would be 1, 5,-5,2-2,4.-4,20, -20
Click here to see answer by ikleyn(52752) |
Question 1155327: hi
i started with the PV formula
0.094^60 = 2.4415
2,000/2.4415
this doesnt make sense
3. Friendly Auto offers Jennifer a car for $2000 down and $300 per month for 5 years. Jason wants to buy the same car but wants to pay cash. How much must Jason pay if the interest rate is 9.4%? (Hint: What is the present value of $300 at 9.4% plus $2,000 paid now?)
Click here to see answer by ikleyn(52752) |
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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, 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