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 – ax2 + 6x – a is divided by x – a.
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Find the remainder when x4 + 1 is divided by x + 1.
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.
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
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.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
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’.
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
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
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
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
