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:

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neela | Student

x^3+kx^2+2x-3 gives a remainder 1 when divided by x+2 gives a remainder 1.

We do the actual operation of division:

x+2) x^3+kx^2 +2x-3( x^2

        x^3 +2x^2

------------------------

x+2)  (k-2)x^2 +2x ( (k-2)x

          (k-2)x^2 +2(k-2)x

--------------------------------------

x+2) (-2k+6)x          - 3   (     (-2k+6)

        (-2k+6)x - 2(-2k+6)

-----------------------------------

                 -4k  +  9 . But this should be equal to 1 as remainder

is  1 by data given.

So -4k+9 = 1.

-4k = 1-9 = -8. 

 k = -8/-4 = 2.

Thus if k = 2, then the given expression  would be x^3+2x^2+x-3  will give a remainder 1 when divided by x+2.

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