Advertisements
Advertisements
प्रश्न
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Advertisements
उत्तर
p(x) = 2x3 − 2x2 + ax − a
Divisor = x − a
∴ take x = a
Remainder = p(a)
2 × a3 − 2 × a2 + a × a − a
= 2a3 − 2a2 + a2 − a
∴ Remainder = 2a3 − a2 − a
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
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.
Using the remainder theorem, find the remainders obtained when x3 + (kx + 8 )x + k is divided by x + 1 and x − 2.
Hence, find k if the sum of the two remainders is 1.
Polynomials bx2 + x + 5 and bx3 − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).
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).
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 3x3 + 7x2 – 5x + 1
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
If x25 + x24 is divided by (x + 1), the result is ______.
