Advertisements
Advertisements
प्रश्न
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
Advertisements
उत्तर
Let p(x) = x2 − 7x + 9
Divisor = x + 1
∴ take x = −1
By remainder theorem,
Remainder = p(−1)
= (−1)2 − 7 × (−1) + 9 =
1 + 7 + 9
= 17
∴ Remainder = 17
APPEARS IN
संबंधित प्रश्न
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
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.
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.
(2x3 − 2x2 + ax − a) ; (x − a)
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
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).
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
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) = 2x3 – 7x2 + 3
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 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.
Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x2 + 7x.
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
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
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
