Write a cubic polynomial that gives a remainder of 4 when it is divided by(x+2)

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A cubic polynomial that gives a remainder of 4 when it is divided by x + 2 can be written as

`P_3 = (x+2)*P_2+ 4` , where `P_2 ` is any quadratic polynomial (can be monomial, binomial or trinomial.)

It can be seen from the expression above that when `P_3` is divided by x + 2, it will result in

`P_3/(x+2) = P_2 + 4/(x+2)`  , so 4 is the remainder.

Let `P_2 = x^2 - 1`

Then `P_3 = (x+2)(x^2 - 1)+ 4 = x^3 + 2x^2 - x - 2 + 4 = `

`x^3 + 2x^2 - x +2` .

A cubic polynomial in question can be `x^3 + 2x^2 - x + 2` .

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