using remainder theorem find the reminder when x^3-6x^2+2x-4 divided by (1-2x)
Answers
Solution :-
1 - 2x = 0
- 2x = - 1
2x = 1
x = 1/2
p(x) = x³ - 6x² + 2x - 4
p(1/2) = (1/2)³ - 6*(1/2)² + 2*(1/2) - 4
= 1/8 - 6*(1/4) + 1 - 4
= 1/8 - 6/4 + 1 - 4
= 1/8 - 3/2 + 1 - 4
Taking L.C.M. of the denominators and then solving it.
= (1 - 12 + 8 - 32)/8
= - 35/8
Remainder is - 35/8
Now, actual division.
- 6x² - 1
_________________
1 - 2x ) x³ - 6x² + 2x - 4 (
12x³ - 6x²
- +
______________
- 11x³ + 2x - 4
+ 2x - 1
- +
_______________
- 11x³ - 3
_______________
Remainder is - 11x³ - 3
Verification :
⇒ - 11x³ - 3
⇒ - 11*(1/2)³ - 3
⇒ - 11*1/8 - 3
⇒ - 11/8 - 3/1
⇒ Taking L.C.M. of the denominator and then solving it.
⇒ (- 11 - 24)/8
⇒ - 35/8
Verified.
Answer:
remainder is -35/8..............................................................