Advertisements
Advertisements
Question
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
Advertisements
Solution
(2x - 1) ⇒ x = `1/2`
When we substirute this value in the polynomial, whatever we get as a remainder (say a) should be added so that polynomial is exactly subtracted by the factor.
`"f"(1/2) = 12 xx (1/2) xx (1/2) xx (1/2) + 16 xx (1/2) xx (1/2) - 5 xx (1/2) - 8 + "a" = 0`
`=> 3/2 + 4 - 5/2 - 8 + "a" = 0`
⇒ a = 5
+ 4 - - 8 + a = Hence answer = 5
APPEARS IN
RELATED QUESTIONS
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
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.
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
