Question

what must be subtracted from 4x^4-2x^3-6x^2+x-1 so that the resulting polynomial is exactly divisible by 2x^2+x-1?

Answer 1

Answer:

$\boxed{4x^4-2x^3-8x^2}$

Step-by-step explanation:

The given expression is :

$4x^4-2x^3-6x^2+x-1$

Let k be subtracted from it .

So :

$4x^4-2x^3-6x^2+x-1-k=2x^2+x-1$

Cancel x - 1 both sides :-

$\implies 4x^4-2x^3-6x^2-k=2x^2$

Transpose k to the other side :-

$\implies k=4x^4-2x^3-6x^2-2x^2$

$\implies k=4x^4-2x^3-8x^2$

Hence this must be subtracted from the given polynomial

Hope it helps ;-)

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