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
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
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.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x3 – 7x2 + 4x + 11
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
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
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
