Advertisements
Advertisements
प्रश्न
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x + 3
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
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
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x3 – 12x2 + 14x – 3; g(x) = 2x – 1
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
