CPhill

As guest points out, not necessarily......Example :

360 / 60 = 6

360 / 10  = 36

I answered this one here :   https://web2.0calc.com/questions/statue-of-liberty

45x^5+6x^4+3x^3+8x+12 by 3x-12

This is certainly an unusual one!!!!

First, we want  to factor the denominator  as 3[x - 4]

Then, we want to divide all the coefficients by 3   [don't forget to include the "missing"  power of x^2....it's coefficient will be 0

[45x^5 + 6x^4 + 3x^3 + 0x^2 + 8x + 12]  / [3 (x - 4)] =

This results in :

[15x^5 + 2x^4 + x^3 + 0x^2 + (8/3)x + 4] / (x - 4)

Now, proceed normally

4  [   15        2        1          0          8/3              4          ]

                  60      248     996      3984          47840/3  

       --------------------------------------------------------------

         15     62      249    996       11960/3      47852/3

And the resultant polynomial  is :

15x^4 + 62x^3 + 249x^2 + 996x + 11960/3  +   remainder of 47852 / 3

21^2=13^2+29^2-2*13*29*cosA      and we're trying to find angle "A"

441  = 169 + 841  - 2(13)(29) cosA

441 = 1010 - 754 cosA     subtract 1010 from each side

-569 =  -754 cosA      divide both sides by -754

569/754  = cosA       we need to use the cosine inverse, here

cos-1 (569/754) = A = about  41°

To find the % discount :

( [Old Price - New Price] / Old Price x 100)  %

 ( [  (27 - 8) / 27 ]  x 100 ) %  =   about 70.37%  discount

25 and 36 share no common factors.....thus 25 / 36   is in lowest terms.....

I'll bet the instructions were to write this with a positive exponent.....if so, we have

x^-2   = 1 / x^2

No prob.......

Press the "2nd" key on the calculator....it's the "asin" key   [arcin, or sine inverse, key ]

(3 - x)^2  =

(x - 3)^2  =

(x - 3) (x - 3)  =

x(x-3) - 3(x - 3) =

x^2 - 3x - 3x + 9  =

x^3 - 6x + 9