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stanbon answered: 57911 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>Next

Travel_Word_Problems/281971: The arrival time t of train B must be at least 5 minutes different from the 4:00 pm arrival time of train A. Express the statement in terms of an inequality invilving an absolute value.
First, I'm not sure if it is mathmatically appropriate to represent the time 4:00 as a real number.
Would the answer be something like:
|4:00-5|>=t
1 solutions

Answer 204773 by stanbon(57984) About Me  on 2010-03-17 11:34:09 (Show Source):
You can put this solution on YOUR website!
The arrival time t of train B must be at least 5 minutes different from the 4:00 pm arrival time of train A. Express the statement in terms of an inequality involving an absolute value.
First, I'm not sure if it is mathmatically appropriate to represent the time 4:00 as a real number.
Would the answer be something like:
|4:00-5|>=t
-----------------------
You want the "distance" from 4:00 to be at least 5 minutes.
----------------------------
|a-b| means "the distance between a and b".
---
Your problem:
|4:00-t| >= 5 minutes
===========================
Cheers,
Stan H.


Probability-and-statistics/281972: The graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardized test is normally distributed?

1 solutions

Answer 204770 by stanbon(57984) About Me  on 2010-03-17 11:18:25 (Show Source):
You can put this solution on YOUR website!
The graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardized test is normally distributed?
---------------------------------------------------
Find the z-value that has right-tail of 10%.
z = invNorm(0.90) = 1.2816
--------------------------------
Find the x-value that corresponds to that z-score:
x = zs + u
x = 1.2816*100 + 500
x = 128.16 + 500
x = 628.16
=================
Cheers,
Stan H.


Probability-and-statistics/281791: With Binomial Distributions and Probability:
In a lottery, each ticket buyer has a 1 in 10 chance of winning a prize. If Steve buys 10 tickets, what is the probability that he will win at least 1 prize? How do you work this problem out?
1 solutions

Answer 204768 by stanbon(57984) About Me  on 2010-03-17 11:13:52 (Show Source):
You can put this solution on YOUR website!
With Binomial Distributions and Probability:
In a lottery, each ticket buyer has a 1 in 10 chance of winning a prize. If Steve buys 10 tickets, what is the probability that he will win at least 1 prize? How do you work this problem out?
-------------------------------
Binomial Problem:
n = 10 ; p = 1/10
---
P(win at least 1) = 1 - P(win none)
----
P(win at least 1) = 1 - (0.9)^10
---
P(win at least 1) = 1 - 0.3487 = 0.6513
========================================
Cheers,
Stan H.


real-numbers/281906: TELL WHICH SET OR SETS THE FOLLOWING NUMBER BELONGS TO: NATURAL NUMBERS, WHOLE NUMBERS, INTEGERS, RATIONAL NUMBERS, IRRATIONAL NUMBERS AND REAL NUMBERS.
-1/3
1 solutions

Answer 204745 by stanbon(57984) About Me  on 2010-03-17 08:37:52 (Show Source):
You can put this solution on YOUR website!
TELL WHICH SET OR SETS THE FOLLOWING NUMBER BELONGS TO: NATURAL NUMBERS, WHOLE NUMBERS, INTEGERS, RATIONAL NUMBERS, IRRATIONAL NUMBERS AND REAL NUMBERS.
-1/3
Rational and therefore, Real
================================
Cheers,
Stan H.


logarithm/281904: use the formula P=Po^ekt. a bacterial culture has an initial population of 10,000. if its population declines to 7000 in 2 hours,
a.) find the exponential model for this data
b.) what will the population be at the end of 4 hours
1 solutions

Answer 204744 by stanbon(57984) About Me  on 2010-03-17 08:36:35 (Show Source):
You can put this solution on YOUR website!
use the formula P=Po^ekt. a bacterial culture has an initial population of 10,000. if its population declines to 7000 in 2 hours,
-------------------
initial population = Po = 10,000
-----
a.) find the exponential model for this data
Find k if t=2 hrs.
7000 = 10,000*e^(k(2))
e^(2k) = 0.7
Take the natural log and solve for "k":
2k = ln(0.7)
k = -0.1783
----------------------
Model: P(t) = 10,000*e^(-0.1783t)
======================================
b.) what will the population be at the end of 4 hours
P(4) = 10,000*e^(-0.1783*4)
P(4) = 10,000*0.49
P(4) = 4900
==================
Cheers,
Stan H.


Probability-and-statistics/281856: A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages µ = 40 on a standardized depression test. The psychologist obtains a sample of n = 36 individuals who are all older than the age of 70. The average depression score for this sample is M = 44.5 with SS = 5040. On the basis of this sample, can the psychologist conclude that depression for elderly people is significantly different from depression in the general population? Use a two-tailed test at the .05 level of significance.
1 solutions

Answer 204740 by stanbon(57984) About Me  on 2010-03-17 08:29:08 (Show Source):
You can put this solution on YOUR website!
A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages µ = 40 on a standardized depression test.
The psychologist obtains a sample of n = 36 individuals who are all older than the age of 70. The average depression score for this sample is M = 44.5 with SS = 5040.
On the basis of this sample, can the psychologist conclude that depression for elderly people is significantly different from depression in the general population? Use a two-tailed test at the .05 level of significance.
---------------------------
Ho: u = 40
Ha: u is not equal to 40
----------------
test stat: t(44.5) = (44.5-40)/[s/sqrt(36)]
---
Note: You say SS=5040. You did not post the standard
deviation of the population or of the sample.
---
Cheers,
Stan H.


Exponential-and-logarithmic-functions/281792: 5log_4⁡2+log_4⁡x


1 solutions

Answer 204715 by stanbon(57984) About Me  on 2010-03-16 22:23:32 (Show Source):
You can put this solution on YOUR website!
Your posted problem is garbled.
Cheers,
Stan H.


Triangles/281782: The measures of the sides of an isosceles triangle are 10, 10, and 4. Find the measure of a base angle to the nearest degree.
a. 23
b. 60
c. 78
d. 85
1 solutions

Answer 204714 by stanbon(57984) About Me  on 2010-03-16 22:21:43 (Show Source):
You can put this solution on YOUR website!
The measures of the sides of an isosceles triangle are 10, 10, and 4. Find the measure of a base angle to the nearest degree.
---------------
Use Law of Cosines:
cos(A) = (b^2 + c^2 - a^2)/2bc
Find the angle opposite 4:
cos(A) = (10^2 + 10^2-4^2)/(2*10*10)
cos(A) = (84)/200 = 0.42
cos^-1(0.42) = 65 degrees
----
Each base angle = (180-65)/2 = 57.5 degrees
================================
Cheers,
Stan H.



a. 23
b. 60
c. 78
d. 85


Triangles/281771: A plane's altitude is 2400 ft. For the pilot, the angle of depression of the base of a control tower is 13 degrees. To the nearest foot, what is the distance from the pilot to the base of the control tower?
a. 2400 ft
b. 31,200 ft
c. 10,396 ft
d. 10,669 ft

1 solutions

Answer 204711 by stanbon(57984) About Me  on 2010-03-16 22:08:28 (Show Source):
You can put this solution on YOUR website!
A plane's altitude is 2400 ft. For the pilot, the angle of depression of the base of a control tower is 13 degrees. To the nearest foot, what is the distance from the pilot to the base of the control tower?
--------------
Draw the picture:
You have a right triangle with
base = x
height = 2400
Angle opposite the height = 13 degrees
-----------------------------------------
Equation:
tan(13) = 2400/x
x = 2400/tan(13)
x = 10395.54 ft.
==================
Cheers,
Stan H.


a. 2400 ft
b. 31,200 ft
c. 10,396 ft
d. 10,669 ft


Polynomials-and-rational-expressions/281778: multiplying polynomials.
(6m^4)(8m^2)
1 solutions

Answer 204708 by stanbon(57984) About Me  on 2010-03-16 22:01:50 (Show Source):
You can put this solution on YOUR website!
multiplying monomials
(6m^4)(8m^2)
---
= 48m^6
==================
Cheers,
Stan H.


Polynomials-and-rational-expressions/281776: Determine the leading term, leading coefficient, and the degree of the polynomial. - x - 4x^2 - 4x^3 - 3x^5 + 4
1 solutions

Answer 204704 by stanbon(57984) About Me  on 2010-03-16 21:59:55 (Show Source):
You can put this solution on YOUR website!
Determine the leading term, leading coefficient, and the degree of the polynomial. - x - 4x^2 - 4x^3 - 3x^5 + 4
------------------------
leading term: -3x^5
leading coefficient: -3
degree of the poly: 5
==========================
Cheers,
Stan H.


Quadratic_Equations/281773: x^1/2*y^1/6*z^1/5
Write as a single radical expression using rational exponents only.
1 solutions

Answer 204699 by stanbon(57984) About Me  on 2010-03-16 21:55:35 (Show Source):
You can put this solution on YOUR website!
x^1/2*y^1/6*z^1/5
Write as a single radical expression using rational exponents only.
----------------------------------------------------
Change all the denominators to 30:
x^(15/30)*y^(5/30)*z^(6/30)
-----------------------------
30th root of (x^16y^5z^6)
=================================
Cheers,
Stan H.


Probability-and-statistics/281562: In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.

1 solutions

Answer 204696 by stanbon(57984) About Me  on 2010-03-16 21:50:12 (Show Source):
You can put this solution on YOUR website!
In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility.
During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of
-------
p-hat(red) = 20/153,348 = 1.304x10^-4
------------
yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135035 = 2.9622x10-5
-------------------
At α = .01, did the yellow fire trucks have a significantly lower accident rate?
One-tail z-test: Critical value = 2.326
(a) State the hypothesis.
Ho: p(red)-p(yellow) = 0
Ha: p(red)-p(yellow) < 0
-------------------------------
(b) State the decision rule and sketch it.
? Not sure what is meant by this.
-------------------------------
(c) Find the sample proportions and z test statistic.
Test statistic:
---
Note: p-bar= (4+20)/(153348+135035) = 8.3223x10^-5;q-bar=1-p-bar
-----------------------
Test statistic
z(1.0078x10^-4) = 1.0078x10^-4/sqrt[(p-bar)(q-bar)/n1 + (p-bar)(q-bar)/n2]
= 2.9610
(d) Make a decision.
Since the test statistic is greater than the critical value, reject Ho.
p(red) is not equal to p(yellow)
------------------------------------------
(e) Find the p-value and interpret it.
p-value = 0.0015 ; Only 0.15% of test results could have provided stronger
evidence for rejecting Ho.
-------------------------
(f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
I'll leave that to you
--------------------
(g) Is the normality assumption fulfilled? Explain.
Show that p(red)n1>5, q(red)n1>5
and p(yellow)n2>5, q(yellow)n2>5
=======================================
Cheers,
Stan H.


Probability-and-statistics/281709: A student takes a 20-question, multiple choice exam with five choices for each question and guesses on each question. Assuming for each question only one of the five choices is correct, what is the mean number of questions the student could get correct by guessing?
1 solutions

Answer 204691 by stanbon(57984) About Me  on 2010-03-16 21:45:20 (Show Source):
You can put this solution on YOUR website!
A student takes a 20-question, multiple choice exam with five choices for each question and guesses on each question. Assuming for each question only one of the five choices is correct, what is the mean number of questions the student could get correct by guessing?
--------------------------------------
Binomial Problem:
n = 20 ; p = 1/5
----
mean = np = (1/5)20 = 4
---------------------------------
Cheers,
Stan H.


Miscellaneous_Word_Problems/281716: A swimming pool can be filled in 12 hours and drained in 20 hours. If the pool is empty and the drain is open, how long will it take to fill the pool?
1 solutions

Answer 204661 by stanbon(57984) About Me  on 2010-03-16 20:03:25 (Show Source):
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A swimming pool can be filled in 12 hours and drained in 20 hours. If the pool is empty and the drain is open, how long will it take to fill the pool?
-----------------
Filling rate: 1/12 job/hr
Drain rate::: 1/20 job/hr
Together rate 1/x job/hr
------------------------------
Equation:
rate - rate = together rate
1/12 - 1/20 = 1/x
Multiply thru by 60x to get:
5x - 3x = 60
2x = 60
x = 30 hrs (time to fill the pool with both pipes open)
===========================================================
Cheers,
Stan H.


Exponential-and-logarithmic-functions/281718: log x - log 4 = -1
1 solutions

Answer 204660 by stanbon(57984) About Me  on 2010-03-16 19:59:27 (Show Source):
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log x - log 4 = -1
---
log(x/4) = -1
x/4 = 10^-1
x = 4/10
x = 2/5
==============
Cheers,
Stan H.


Exponential-and-logarithmic-functions/281717: 2 log 3x - log 9 = 1
1 solutions

Answer 204658 by stanbon(57984) About Me  on 2010-03-16 19:57:27 (Show Source):
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2 log(3x) - log 9 = 1
---
2[log(3)+log(x)] - 2log(3) = 1
2log(3) + 2log(x) - 2log(3) = 1
2log(x) = 1
log(x) = 1/2
x = 10^(1/2)
x = sqrt(10)
=====================
Cheers,
stan H.


Linear-systems/281713: 4/7=8/x
1 solutions

Answer 204657 by stanbon(57984) About Me  on 2010-03-16 19:49:27 (Show Source):
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4/7=8/x
-----------------------
Invert both sides to get:
x/8 = 7/4
Multiply both sides by 8 to solve for "x":
x = 2*7
x = 14
=====================
Cheers,
Stan H.


Sequences-and-series/281707: how do you find the 10th term of (x+y)^20?
1 solutions

Answer 204654 by stanbon(57984) About Me  on 2010-03-16 19:42:14 (Show Source):
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how do you find the 10th term of (x+y)^20?
-----------------
10th term
= 20C11x^11y^9
----
= 167960x^11y^9
====================
Cheers,
Stan H.


Exponential-and-logarithmic-functions/281703: 2 to the 6 times 2 to the 2
1 solutions

Answer 204653 by stanbon(57984) About Me  on 2010-03-16 19:34:29 (Show Source):
You can put this solution on YOUR website!
2 to the 6 times 2 to the 2
------
2^6*2^2 = 2^8 = 256
================================
Cheers,
Stan H.


Linear_Equations_And_Systems_Word_Problems/281697: I'm having problems solving this word problem. I need two different plans with equations. I can't figure out the equations for this problem. Is x the same for both equations? Select an investment plan for a family with a child that is x years old and has y dollars to investment.
1 solutions

Answer 204652 by stanbon(57984) About Me  on 2010-03-16 19:31:17 (Show Source):
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I need two different plans with equations. I can't figure out the equations for this problem. Is x the same for both equations? Select an investment plan for a family with a child that is x years old and has y dollars to investment.
------------------------
I assume you mean the plan is x years old.
-------------------------
Simple Interest investment: Value of an investment of y dollars after x years :
A(x) = y(1+rx) where r is the annual rate of interest.
-------------------------
Compound Investment:Value of an investment of y dollars after x years:
A(x) = y(1+(r/n))^(nx) where n is the number of times the money is
compounded each year.
==============================
Cheers,
Stan H.


Geometry_Word_Problems/281694: find a trinmoial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3meters. find A(3)
1 solutions

Answer 204650 by stanbon(57984) About Me  on 2010-03-16 19:23:56 (Show Source):
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find a trinomial A(x) that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3meters.
------------
A(x) = (3x+2)(2x+3) = 6x^2 + 13x + 6
-------------
Find A(3) = (11)(9) = 99
=============================
Cheers,
Stan H.


Rectangles/281689: The length of a rectangle is 3 centimeterss less than twice its width. What is the width of the rectangle if the perimeters is 39 centimeters?
1 solutions

Answer 204649 by stanbon(57984) About Me  on 2010-03-16 19:19:48 (Show Source):
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The length of a rectangle is 3 centimeterss less than twice its width. What is the width of the rectangle if the perimeters is 39 centimeters?
------------------------------------------
P = 2(width + length)
39 = 2(w + 2w-3)
39 = 2(3w-3)
13 = 2(w-1)
3w= 15
w = 5 (width)
===========
Cheers,
Stan H.


percentage/281692: 8 is increased by 60%

1 solutions

Answer 204647 by stanbon(57984) About Me  on 2010-03-16 19:14:46 (Show Source):
You can put this solution on YOUR website!
8 is increased by 60%
----------
8 + 0.60*8 = 1.6*8 = 12.8
=============================
Cheers,
Stan H.


Geometry_Word_Problems/281693: THE WIDTH OF A RECTANGULAR PLAYGROUND IS 2x-5 FEET, AND THE LENGTH IS 3x+9 FEET. WRITE A POLYNOMINAL P(x) THAT REPRESENTS THE PERIMETER THEN EVALUATE THIS OERAMETER IF x IS 4 FEET.
1 solutions

Answer 204645 by stanbon(57984) About Me  on 2010-03-16 19:12:36 (Show Source):
You can put this solution on YOUR website!
THE WIDTH OF A RECTANGULAR PLAYGROUND IS 2x-5 FEET, AND THE LENGTH IS 3x+9 FEET. WRITE A POLYNOMINAL P(x) THAT REPRESENTS THE PERIMETER THEN EVALUATE THIS OERAMETER IF x IS 4 FEET.
------------------------------------
Perimeter = 2(width + length)
P = 2(2x-5+3x+9)
P = 2(5x+4)
----------------
P(4) = 2(24) = 48 feet
========================
Cheers,
Stan H.


logarithm/281691: x^3/100 = x^log x
Can you solve for ALL values of x, i found that x=10 but can't find the rest of the solutions thank you
1 solutions

Answer 204643 by stanbon(57984) About Me  on 2010-03-16 19:08:17 (Show Source):
You can put this solution on YOUR website!
x^3/100 = x^log x
---
x^(3/100) = x^(log(x))
----
log(x) = 3/100
x = 10^(3/100)
x = 100th root of 10^3
x = 100th root of 1000
============================
Cheers,
Stan H.


Probability-and-statistics/281627: several factors influence the value obtained for a t statistic. Some factors affact the numerator of the t statistic and others influence the size of the estimated standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or denominator of the t statistic and determine whether the effect would be to increase the value of t (farther from zero) or decrease the value of t ( closer to zero ). In each case, assume that all other factors remaine constant .
a - Increase the variability of the scores.
b - Increase the number of scores in the sample.
c - Increase the difference between the sample mean and the population mean.
1 solutions

Answer 204642 by stanbon(57984) About Me  on 2010-03-16 19:04:44 (Show Source):
You can put this solution on YOUR website!
several factors influence the value obtained for a t statistic. Some factors affact the numerator of the t statistic and others influence the size of the estimated standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or denominator of the t statistic and determine whether the effect would be to increase the value of t (farther from zero) or decrease the value of t ( closer to zero ). In each case, assume that all other factors remaine constant .
---
General Form:
t(x) = (x-u)/[s/sqrt(n)]
-----------------------------
a - Increase the variability of the scores. As s increases, t decreases.
---------------------------------------
b - Increase the number of scores in the sample. As n increases, t increases.
-----------------------------
c - Increase the difference between the sample mean and the population mean.
As the difference increases t increases.
=============================================
Cheers,
Stan H.


Exponents/281503: (3m^1n^4)^2 (2m^3n^-5)^4 Explain and show solution please.
1 solutions

Answer 204504 by stanbon(57984) About Me  on 2010-03-16 13:03:12 (Show Source):
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(3m^1n^4)^2 (2m^3n^-5)^4
-----------
(9m^2n^8)(16m^12n^-20)
-----------
144m^14n^-12
-----------
144m^14/n^12
====================
Cheers,
Stan H.


Trigonometry-basics/281505: I need to find the exact value of this expression +1-cos%5E2+%2820+degrees%29-cos%5E2+%2870+degrees%29 using fundamental identities or the Complementary Angle Theorem. I thought maybe the Complementary Angle Theorem would help but I am not sure how. Thank you for any help. :) By the way, both cosines are squared but when I preview, it does not look like they show up.
1 solutions

Answer 204503 by stanbon(57984) About Me  on 2010-03-16 12:58:53 (Show Source):
You can put this solution on YOUR website!
I need to find the exact value of this expression +1-cos%5E2+%2820+degrees%29-cos%5E2+%2870+degrees%29 using fundamental identities or the Complementary Angle Theorem. I thought maybe the Complementary Angle Theorem would help but I am not sure how. Thank you for any help. :) By the way, both cosines are squared but when I preview, it does not look like they show up.
-------------------------
(1 - cos^2(20)) - cos^2(70)
=====
Note: 1-cos^2(2) = sin^2(2)
=====
= sin^2(20) - cos^2(70)
=====
Note: sin(20) = cos(70)
=====
= cos^2(70) - cos^2(70)
= 0
===============================
Cheers,
Stan H.


Polynomials-and-rational-expressions/281507: Simplify by removing factors of 1 2z-8/4-2?
1 solutions

Answer 204501 by stanbon(57984) About Me  on 2010-03-16 12:53:37 (Show Source):
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Simplify by removing factors of 1 2z-8/4-2?
That's confusing. You need some parentheses in your post.
Cheers,
Stan H.


Complex_Numbers/281506: 15x to the 3rd power + 42x-9? i know thw greatest common factor is 3 but i need a product and a sum????
1 solutions

Answer 204499 by stanbon(57984) About Me  on 2010-03-16 12:51:38 (Show Source):
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15x to the 3rd power + 42x-9? i know thw greatest common factor is 3 but i need a product and a sum????
-------------
15x^3 + 42x - 9
---------------------
= 3(5x^3 + 14x - 3)
=========================
Cheers,
Stan H.