How do i find k when x^3+kx^2+2x-3 is divided by X+2 and the remainder is 1

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let f(x) = x^3 + kx^2 + 2x -3

When we devide f(x) with (x+2) th result will be a function (let it be R(x) and a remainder of 1:

Then we could write:

==> f(x)= (x+2) * R(x) + 1

Let us substitute with x= -2:

==> f(-2) =...

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let f(x) = x^3 + kx^2 + 2x -3

When we devide f(x) with (x+2) th result will be a function (let it be R(x) and a remainder of 1:

Then we could write:

==> f(x)= (x+2) * R(x) + 1

Let us substitute with x= -2:

==> f(-2) = (-2+2)* R(-2) + 1

==> f(-2) = 1.........(1)

But, f(x) = x^3 + kx^2 + 2x -3

Let us sustitute x=-2 in f(x) .

==> f(-2) = -8 + 4k - 4 -3 = 1

==> 4k -15 = 1

==> 4k = 16

==> k= 4

==> f(x) = x^3 + 4x^2 + 2x - 3

==> f(x) = (x+2)(x^2 + 2x -2) + 1

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