+0  
 
+1
68
8
avatar+1857 

Another one >.<

would it be 5/8 for 8x-5

RainbowPanda  Sep 19, 2018
edited by RainbowPanda  Sep 19, 2018
 #1
avatar+3189 
+3

\(\frac{(80x^3-50x^2+7)}{(8x-5)}\). First, divide the leading coefficients of \(80x^3-50x^2+7\mathrm{\:and\:the\:divisor\:}8x-5\), so this means that: 

\(\frac{80x^3}{8x}\), which is \(10x^2.\) That is our quotient, and now we have to find the remainder. So, multiply 8x-5 by 10x^2, to attain \(80x^3-50x^2.\) Now, subtract this result from \(80x^3-50x^2+7\) , to get \(7\) as our new remainder. Therefore, \(\frac{(80x^3-50x^2+7)}{(8x-5)}=\boxed{10x^2+\frac{7}{8x-5}}\).

Wait, is this good? IDK.

smileysmiley

tertre  Sep 19, 2018
 #2
avatar+1857 
+2

That's definitely the right answer but not how it's supposed to be solved, but thanks! I think I got it ^-^

RainbowPanda  Sep 19, 2018
 #3
avatar+3189 
+2

Yeah, I didn't use synthetic division. 

tertre  Sep 19, 2018
 #5
avatar+90023 
+3

That's OK, tertre.....synthetic division is a little bit tricky in this kind of problem when the linear divisor  is in the form ax +/- b    !!!

 

 

 

cool cool cool

CPhill  Sep 19, 2018
 #4
avatar+90023 
+3

Set 8x  - 5  = 0  ⇒    x =  5/8....this is what we need to divide by

 

Note that the polynomial is really   80x^3  - 50x^2  + 0x   + 7

 

5/8  [  80      -50       0        7  ]

                     50       0        0

         _____________________

         80         0        0         7

 

The remainder is correct

 

The apparent remaining polynomial is  80x^2

 

Note....RP...that all we really need to do to find the correct remaining polynomial is just to divide  the apparent remaining polynomial  by   the "a"  coefiicient  of the  divisor, ax - b.....in this case.....ax - b  = 8x  - 5...so we can divide

 

80x^2  by   8  = 10x^2  and this is the correct residual polynomial

 

So...the answer   10x^2 R [ 7 /(8x - 5) ] 

 

Does that help????

 

 

cool cool cool

CPhill  Sep 19, 2018
edited by CPhill  Sep 19, 2018
 #6
avatar+1857 
+2

Yes I did it a different way if that's alright. 5/8| 10   -25/4   0   7/8

                                                                                 25/4   0     0

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

                                                                          10   0     0     7/8

10x^2+7/8x-5

RainbowPanda  Sep 19, 2018
 #7
avatar+90023 
+2

Different roads....same answer....good job  !!!

 

[You divided the polynomial by 8 right away.....and realized that the  "7"  in the denominator of the "remainder fraction" represented the true remainder....if you like that method better, stick with it...I just learned it a different way....at least you understand these, now....that's the important thing  !!! ] 

 

 

cool cool cool

CPhill  Sep 19, 2018
 #8
avatar+3189 
+3

Wow! Great Solution, CPhill! smiley

tertre  Sep 19, 2018

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