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?
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
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.
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’.
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.
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
Find without division, the remainder in the following :
x3 + 8x2 + 7x- 11 is divisible by (x+4)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
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
If x25 + x24 is divided by (x + 1), the result is ______.
