f(3x+2) = 27x^3+30x+9
To
determine
f(x).
Solution:
3x+2|27x^3+30x+9(9x^2
- 6x +14
27x^2+18x^2
------------------------------
-18x^2+
30x
-18x^2
-12x
--------------------------
42x +9
42x+28
---------------------------
-19
.............................R1.
Again
devide 9x^2-14x+14 by 3x+2.
3x+2|9x^2-6x+14( 3x
-4.
9x^2+6x
------------------------
-12x+14
-12x-8
----------------------------
22...........................R2
Again divide
the quotient by 3x-4 by 3x+2:
3x-2|3x-4( 1 =
Rsay.
3x+2
---------------------
-6
--------------R3
Therefore
f(3x+2)
= Rt^3+R1*t^2+R2 * t+R1, where t =3x+2 and R1 ,R2,R3 are the successive
remainders.
So f(3x+2) = (3x+2)^2 -6(3x+2)^2 + 22(3x+2)
-19.
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