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# Synthetic division

0
262
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+2448

Last 2

Edit: I solved the first one, it's x^2-9x-9 R=0/7x+8

Sep 19, 2018
edited by RainbowPanda  Sep 19, 2018

#1
+2448
0

Is the last one -4/9| 1   49/9  -7/9   -34/3   -41/9

-4/9  -20/9   4/3      40/9

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

1    5       -3      10       -1/9

n^3+5n^2-3n-10+ -1/9n+4

Sep 19, 2018
#2
+101871
+2

Correct,RP!!!...good job  !!!

[Just a note...remember to write the remainder as   -1 /[9n + 4]....what you have is  -1/9n + 4...which translates to :

(-1/9) n   +  4 .... ]

Otherwise....very nice!!!

Sep 19, 2018
#3
+4296
+1

Divide 9n^4+49n^3-7n^2-102n-41 by -4/9, 9  49  -7 -102 -41 divided by -4/9,

Solving synthetic, 9x^3+45x^2-27x-90-1/x-4/9?

Is it wrong?

Sep 19, 2018
edited by tertre  Sep 19, 2018
#4
+101871
+2

Almost, terte

9n + 4   = 0   ⇒   n  = -4/9    and this is what we need to divide by

-4/9   [  9    49    - 7   - 102    - 41  ]

-4    -20      12       40

________________________

9    45     -27     -90      - 1

Your remainder of  -1   is correct

The apparent residual plynomial is    9n^3  + 45n^2  - 27n  - 90

Note....to find the correct residual polynomial,  divide  the  apparent  residual polynomial by the  "9"  in the linear divisor of  9x - 4

So...we actually have

n^3  + 5n^2  - 3n  - 10  R ( -1/ [ 9n  - 4 ] )

To see why this is true...note the polynomial division  ;

n^3

(9n - 4)  [ 9n^4.........            ]

-(9n^4)

___________

etc. ........

Note that the first term is  n^3 .....not 9n^3...

CPhill  Sep 19, 2018
#5
+4296
+1

Oh, thank you, CPhill! My small error, oops!

Sep 19, 2018