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`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
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’.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
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’.
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (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).
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
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 the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
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.
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
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)?
