#2**+2 **

We try the values y= 1, 2, 3, 4, 5, 6,...and so on.

For the function to have an upper bound, the coefficients of the polynomial when the original polynomial divided by (y) has to be positive. I recommend using Sythetic Division to divide the polynomial with the number.

Trying y=1, gives us a polynomial that alternates in signs. Same with y=2. Yet, y=3 gives us a polynomial with all positive coefficients. y=3: Answer

tertre Sep 14, 2019

#10**0 **

Testing the values with y=1, y=2, y=3, y=4 yields negative value by using Synthetic Division. Yet, we can realize something. The -25x^3 is really messing up the positive values, so we need to find a value larger than 25. Since 6*4=24, that won't work, yet y=7 will work since 7*4=28, which is greater than 25.And yes, y=7 does work.

tertre
Sep 15, 2019

#11**+1 **

When i solve 6 for 4 0 -25 -5 -13 i as well get all postitive vaules, dnt i need to find the lowest value which gives all postitive or all negatitive values?

jjennylove
Sep 15, 2019

#13**+1 **

Tertre might have typoed, yet I think he forgot the 0x^2. This is really important! Check three just to make sure. Three should work.

neworleans06
Sep 15, 2019

#14**+1 **

Yes, you stop when there are all positive values. Feel free to message me at any time!

neworleans06
Sep 15, 2019

#15**0 **

i jsut checked three as well and it worked , the answer must be 3 right? since its the lowest value before they all turn into a mix of pos and neg values? Thank you so much for your help!

jjennylove
Sep 15, 2019

#2**0 **

We try the values y= 1, 2, 3, 4, 5, 6,...and so on.

For the function to have an upper bound, the coefficients of the polynomial when the original polynomial divided by (y) has to be positive. I recommend using Sythetic Division to divide the polynomial with the number.

Trying y=1, gives us a polynomial that alternates in signs. Same with y=2. Yet, y=3 gives us a polynomial with all positive coefficients. y=3: Answer

Guest Sep 14, 2019

#10**0 **

Testing the values with y=1, y=2, y=3, y=4 yields negative value by using Synthetic Division. Yet, we can realize something. The -25x^3 is really messing up the positive values, so we need to find a value larger than 25. Since 6*4=24, that won't work, yet y=7 will work since 7*4=28, which is greater than 25.And yes, y=7 does work.

tertre
Sep 15, 2019

#11**+1 **

When i solve 6 for 4 0 -25 -5 -13 i as well get all postitive vaules, dnt i need to find the lowest value which gives all postitive or all negatitive values?

jjennylove
Sep 15, 2019

#13**+1 **

Tertre might have typoed, yet I think he forgot the 0x^2. This is really important! Check three just to make sure. Three should work.

neworleans06
Sep 15, 2019

#14**+1 **

Yes, you stop when there are all positive values. Feel free to message me at any time!

neworleans06
Sep 15, 2019

#15**0 **

i jsut checked three as well and it worked , the answer must be 3 right? since its the lowest value before they all turn into a mix of pos and neg values? Thank you so much for your help!

jjennylove
Sep 15, 2019

#4**+2 **

Divide each term by 3

1, -7/3, 5/3, -1

Remove the first term and change any minuses to pluses

7/3, 5/3/ 1

1) take the largest value and add 1 to it → 7/3 + 1 = 10/3

2) Sum the values = 5 .....compare this with 1 and take the larger value = 5

Take the smaller of (1), (2)

The upper bound is 10/3

See this graph : https://www.desmos.com/calculator/1mf8fqbard

However....I think that you are using the syntethic division test to find the greatest integer that is an upper bound.....this should be 3

Test 2

2 [ 3 -7 0 5 -3]

6

_______________

3 -1 we get a negative so we can stop

Test 3

3 [ 3 - 7 0 5 -3]

9 6 18 69

_______________

3 2 6 23 66 we ge all positives....so 3 is the largest integer upper bound

CPhill Sep 14, 2019

#9**0 **

im not sure if you remember but this is the way i was talking about for the other question posted above, because i didnt feel like 7.25 fit properly , do u think maybe the answer would then be 13? Thank you as well for your help!

jjennylove
Sep 15, 2019

#16**+2 **

f(x) = 4x^4 - 25x^2 -5x - 13

Test 1 using synthetic division

1 [ 4 0 -25 -5 -13 ]

4 4

______________________

4 4 -21 stop

Test 2

2 [ 4 0 -25 - 5 -13 ]

8 16

________________________

4 8 -9 stop

Test 3

3 [ 4 0 -25 -5 -13 ]

12 36 33 84

___________________________

4 12 11 28 71 all are positive......3 is the upper bound

CPhill Sep 15, 2019