Advertisements
Advertisements
Question
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1
Solution
Given, p(x) = 4x3 – 12x2 + 14x – 3 and g(x) = 2x – 1
Here, zero of g(x) is `1/2`.
When we divide p(x) by g(x) using remainder theorem, we get the remainder `p(1/2)`.
∴ `p(1/2) = 4(1/2)^3 - 12(1/2)^2 + 14(1/2) - 3`
= `4 xx 1/8 - 12 xx 1/4 + 14 xx 1/2 - 3`
= `1/2 - 3 + 7 - 3`
= `1/2 + 1`
= `(1 + 2)/2`
= `3/2`
Hence, remainder is `3/2`.
APPEARS IN
RELATED QUESTIONS
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Using the Remainder Theorem find the remainders obtained when ` x^3 + (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.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
If ( x31 + 31) is divided by (x + 1) then find the remainder.
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 x51 + 51 is divided by x + 1, the remainder is ______.
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
