Question

What must be added to 4x^4 + 2x^3 – 2x^2 + x - 1 so that the resulting polynomial
is divisible by x^2 – 2x - 3?​

Answer 1

Answer:

-91x-89 should be added to the polynomial

Answer 2

The resulting polynomial $4x^4 + 2x^3 - 2x^2 -60x +64$ is divisible by g(x) $x^2- 2x - 3$

Step-by-step explanation:

given p(x) = $4x^4 + 2x^3-2x^2 + x - 1$

g(x) = $x^2- 2x - 3$

on dividing p(x) by g(x)

we get the

remainder = -61x+65

now , we have to add the remainder  in the p(x)

we get

$4x^4 + 2x^3 - 2x^2 + x - 1 -61x +65$

$4x^4 + 2x^3 - 2x^2 -60x +64$

hence , the resulting polynomial $4x^4 + 2x^3 - 2x^2 -60x +64$ is divisible by g(x) $x^2- 2x - 3$

#Learn more:

What must be added to the polynomial 4x^4-2x^3-6x^2+x-5 so that the result is exactly divisible by 2x^2+x-1

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