Question

what number should be added to 27x^3-54x^2+36x-11 so that the resulting polynomial is divisible by 3x-2 ?

pls anyone tell.....
i will mark as brainliest
pls pls its urgent

Answer 1

By remainder theorem,
3x-2=0
x=2/3
Lets add a variable 'k' to the polynomial to find it out.
New Polynomial = 27x^3-54x^2+36x-11+k

By Remainder Theorem, if we put x=2/3, it must be equal to 0 if 3x-2 is a factor of it.

Putting x=2/3
27(2/3)^3-54(2/3)^2+36(2/3)-11+k=0

On simplification we get,
8-24+24-11+k=0
-3+k=0
k=3.
Hence, The number to be added to the Polynomial is 3. Ans.

Answer 2

Answer:

By remainder theorem,

3x-2=0

x=2/3

Lets add a variable 'k' to the polynomial to find it out.

New Polynomial = 27x^3-54x^2+36x-11+k

By Remainder Theorem, if we put x=2/3, it must be equal to 0 if 3x-2 is a factor of it.

Putting x=2/3

27(2/3)^3-54(2/3)^2+36(2/3)-11+k=0

On simplification we get,

8-24+24-11+k=0

-3+k=0

k=3.

Hence, The number to be added to the Polynomial is 3. Ans.