Question

using remainder theorem , find the reminder when 4x³-12x²+11x-5 is divided by (2x-1)​

Answer 1

Answer:

Hey mate see this for your answer

Answer 2

GIVEN

P(x) = 4x³-12x²+11x-5

g(x) = 2x - 1

TO FIND :- Remainder by Remainder Theorem

SOLUTION

The Remainder theorem states that when zero of g(x) is replaced with that of varaible in p(x) the result we get is the remainder when we will divide p(x) by g(x).

Now zero of g(x)

g(x) = 2x - 1

=> g(x) = 2x - 1 [x such that the polynomial will be zero]

=> 2x - 1 = 0

=> 2x = 1

=> x = 1/2

We can put this value in p(x) ,

p(x)= 4x³-12x²+11x-5

=> p(1/2) = 4 (1/2)^3 - 12 (1/2)^2 + 11(1/2) - 5

= 4×1/8 - 12×1/4 + 11/2 - 5

= 1/2 - 3 + 11/2 - 5

= 6 - 3 - 5

= 6 - 8

= - 2 (ANS)

Hence the remainder will be -2 by remainder Theorem.