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
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
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.
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x – 2
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
