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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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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