1.

Find the remainder when x cube minus pX square + 6 x minus p is divided by x minus p

Answer» SOLUTION:- >>>
1-2x = 6
-2x = -1
x = 1/2
p(x) = x^3 - 6x^2 +2 x -4
p(1/2) = (1/2)^3 - 6 x (1/2)^2+ 2 x (1/2)-4
= 1/8 - 6x (1/2) +1-4
= 1/8 - 6/4 +1-4
= 1/8 - 3/2 + 1-4

Taking L.C.M. of the denometors and then solving it.

= (1-12 + 8-32)/8
= -35/8
Remainder is = 35/8
Now, ACTUAL division.
-6x^2-1
____________________
(1-2x) x^3 - 6x^2 + 2 x -4
12x^3 - 6x^2
- +
____________________
- 11x^3 + 2x -4
+ 2x -1
- +
____________________
- 11x^3 - 3

..Remainder is 11x^3 - 3
Verification,
=>> -11x^3 - 3
=>> -11 x (1/2)^3 -3
=>> -11 x 1/8 - 3/1
=>> Taking L.C.M of the denomitor and then solving it.
=>> (-11 - 24)/ 8
=>> -35/ 8
Verified.
I hope it's HELP U


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