Advertisements
Advertisements
Question
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
Options
6
– 6
– 3
0
Advertisements
Solution
f(x) = 2x3 – x2 – 3x + 5
g(x) = 2x + 1
Let 2x + 1 = 0,
then x = `(-1)/(2)`
Then remainder will be
`f((-1)/(2)) = 2((-1)/(2))^3 - ((-1)/(2))^2 -3((-1)/(2)) + 5`
= `2 xx (-1)/(8) - (1)/(4) + (3)/(2) + 5`
= `(-1)/(4) - (1)/(4) + (3)/(2) + 5`
= `(-1 -1 + 6 + 20)/(4)`
= `(24)/(4)`
= 6
∴ Remainder = 6.
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
