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

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.