Question

Find what must be subtracted from the polynomial 2x4-4x3-4x+3 so that the
obtained polynomial becomes divided by x2+x+1​



Pls someone answer fast to get points

Answer 1

Answer:

-2x - 1 must be subtracted from p(x) to get a polynomial which is divisible by g(x).

Step-by-step explanation:

1st Polynomial : p(x) = $2x^4-4x^3-4x+3$

2nd Polynomial: g(x) = $x^2+x+1$

To find: A polynomial which is subtracted from 1st Polynomial to get a polynomial which is divisible by 2nd polynomial.

let, say p(x) is a dividend which is not divisible by g(x).

we need to find remainder which is subtracted from p(x) so that resulting polynomial become divisible by g(x).

Division is done in the pic.

We get,

Quotient = 2x² - 6x + 4

Remainder = -2x - 1

Therefore, -2x - 1 must be subtracted from p(x) to get a polynomial which is divisible by g(x).