Advertisements
Advertisements
प्रश्न
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Advertisements
उत्तर
Let the number to be subtracted be k and the resulting polynomial be f(x).
So, f(x) = x3 + 3x2 – 8x + 14 – k
It is given that when f(x) is divided by (x – 2), the remainder is 10.
∴ f(2) = 10
(2)3 + 3(2)2 – 8(2) + 14 – k = 10
8 + 12 – 16 + 14 – k = 10
18 – k = 10
– k = 10 – 18 = – 8
k = 8
Thus, the required number is 8.
APPEARS IN
संबंधित प्रश्न
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
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’.
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
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).
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
