Advertisements
Advertisements
Question
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Advertisements
Solution
Let f(x) = x3 + 2x2 – kx + 4
x – 2 = 0 `\implies` x = 2
On dividing f(x) by x – 2, it leaves a remainder k.
∴ f(2) = k
(2)3 + 2(2)2 – k(2) + 4 = k
8 + 8 – 2k + 4 = k
20 = 3k
`k = 20/3 = 6(2)/3`
APPEARS IN
RELATED QUESTIONS
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
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).
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
