Advertisements
Advertisements
Question
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Advertisements
Solution
Let p(x) = x31 + 31.
Divisor = x + 1
∴ Let x = −1
By remainder theorem
Remainder = p(−1)
= (−1)31 + 31
= −1 + 31
= 30
Thus, the remainder when (x31 + 31) is divided by (x + 1) is 30.
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 2x2 – 4x – 1; g(x) = x + 1
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
What is the remainder when x2018 + 2018 is divided by x – 1
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
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 6x2 + 2x – 4, g(x) = `1 - 3/2 x`
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
