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Using EP's answer of R = -22

We should get the same answer by subbing 3 inito the polynomial....so...

(3)^3 + (3)^2 - 46(3) + 80 =

27 + 9 -  138 + 80 =

116 - 138 =

-22       ......Magic !!!!!

I'm using Java for it i know im suppose to check if the square is a palindrome and by that i should have an array with the values and a loop to reverse the order. If they match before and after then it is a palindromic square. But i am confused about the base is the base 1-20? and then what does the integers mean? what are they?

                  x^2+4x-34       -  22/(x-3)

x-3  |  x^3+x^2-46x+80

          x^3 -3x^2

        _______________

                  4x^2-46x

                  4x^2-12x

                _____________

                          -34x+80

                          -34x+102

                           __________

                (remainder)  -22

Basically with remainder  -22/(x-3)     then  p(3)  will equal -22

See cphill's explanation/answer here for the second part:

https://web2.0calc.com/questions/what-does-this-mean_10

Error interval is

15.375  ≤  x <  15.385

Error interval  is

3.65 ≤ x < 3.75

5. Is done similarly

Remember that if  x - a is a factor.....then a is a root.....in other words...P(a) will equal 0

So....for x + 6     we can write   [ x - (-6) ]

And   "a" =  - 6

So....put -6 into the polynomial....if you get 0,  then x + 6 is a factor

Do the same thing for  (2)  (3) and (4)

If you are confused....let me know....this IS a little tricky  !!!!

Here's how to do the first one, GM

Evaluate    - 6 , 4, 8  and - 2   in the polynomial   [ one at a time, of course ]

Whichever gives you a 0   [ maybe more than one ]  will be the answer(s)

For example....if we put -6 into the polynomial and get 0,  then  [ x - (-6)  ]    = x + 6  will be an answer

If you have any questions.....let me know....

Malachai's  income is in the third row of the table......go across to Head of Household column to see Malachai owes  4199 in taxes....

your question did not state how much was withheld from his pay, so I cannot say if he owes.... or gets a refund.

thanks man

This is known as the "Remainder Theorem"

It says that   if we divide some polynomial P(x)  by   x - a, then the remainder will be equal to  P(a)

Cutting through the gobbledegook....let's look at an example

Suppose we divide  x^2 - x - 6     by    x - 3 

We have that

           x  + 2

x - 3 [  x ^2 - x - 6 ] 

           x^2  - 3x

           __________ 

                   2x - 6

                   2x - 6 

                  ______

                          0

Note that the remainder = 0

So....a = 3

And P(3)  =  (3)^2 - 3 - 6   =   0    ......the same as our remainder  !!!!! 

So..in your problem

a = 7   

p(x)   was divided by   x - a  and the remainder was 11

Which means that    p(7)   also =   11

(7x +5)(x-2)

P(x) / (x-7)  = x + 11/(x-7)      (given)  If you multiply both sides of this equation by (x-7) you will fid p(x)

p(x) =  x (x-7)   + 11

       = x^2 - 7x + 11      then put 7 in for 'x'  to find p(7) =  11

              x^2    + 2x   + 7

x + 5  [   x^3  +  7x^2  + 17x   +  41 ]

              x^3  +  5x^2

             __________________________

                          2x^2  + 17x

                          2x^2  + 10x

                         __________________

                                       7x   +  41

                                       7x  +   35

                                       _________

                                                     6

So  .....    x^2 + 2x + 7   R  6 / [ x + 5 ]

             2x^2  - 5x + 7

x - 3 [   2x^3 - 11x^2 + 22x   -  25 ]

            2x^3 -  6x^2

           ________________________

                       -5x^2  + 22x

                       -5x^2  + 15x   

                      __________________

                                    7x  - 25

                                    7x -  21

                                _________

                                          - 4

So....  2x^2 - 5x + 7 R  -4 / [ x - 3 ]

Thanks so much for your help. For the first answer, I worked the problem out myself too and I got the same answer so I believe I figured it out. My math teacher is new and can't really teach the material to the class that well. I thank you again for your help. :)

Here :

https://web2.0calc.com/questions/help-please_73081

Assuming that we can have empty boxes

Let k  = the number of balls

Let n = the number of boxes

The total ways  =

C ( k + n - 1 , n - 1 )    =

C ( 6 + 3 - 1 , 3 - 1 )  =

C ( 8 , 2 )  =

28 ways

What is the average of all the odd numbers between 20 and 50

EDIT

In the other problem here : https://web2.0calc.com/questions/help-please_8228

Sue's age was found to be 12

So....Sid is 18

Well, I can barely read the small print on your form W-2.

Obviously, her income(before taxes) is plain enough to see as $34,854.00

Box 4 seems to read: Social Security Tax. If that is correct, my understanding is that the tax rate for 2018 on any income below $128,400 is 6.2%. If you multiply her gross income of $34,854.00 x 0.062 =$2,160.95 - which should be the tax in Box 4. The amount in Box 4 of $2,164.44 seems to have been calculated at 6.21%, which is a very small difference of $3.49. I hope that is correct. Good luck to you.

APY =[1 + 3.65%/12]^12

APY =[1 + 0.0365/12]^12

APY =[1.00304166667]^12

APY =1.0371168481 - 1

APY =0.0371168481 x 100

APY =3.71%

OK.....Mr. "SHADOW"

              3x      +  5

x + 4  [   3x^2  + 17 x   + 25  ]

              3x^2  + 12x

             _________________

                          5x   +  25 

                          5x  +  20

                         ___________  

                                     5

So.....     3x + 5    R   5 /  [ x + 4 ]

Second one

             5x   - 1

x - 8    [ 5x^2 -  41x + 3      ]

             5x^2 - 40x

            ______________

                        -1x   + 3

                        -1x   + 8

                      __________

                                -5

So...      5x - 1   R   -5 / [ x - 8 ]

f (f(x) ) =

sqrt [  sqrt (x - 3) - 3  ]

sqrt (x - 3)  - 3     must be  ≥ 0

So...

sqrt ( x - 3) - 3 ≥ 0

sqrt (x - 3) ≥ 3        square both sides

x - 3 ≥ 9

x ≥ 12

So.....12 is the smallest real number in the domain