Question

If x3 - 3x2 + 4x +k is exactly divisible by x – 2 then k =
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Answer 1

k = -4.

Step-by-step explanation:

x3 - 3x2 + 4x +k is exactly divisible by x-2. So x-2 is a factor of x3 - 3x2 + 4x +k.

So x-2 = 0. Hence x = 2.

Substituting x = 2 in x3 - 3x2 + 4x +k, we get:

2^3 - 3(2^2) + 4(2) + k = 0

8 - 12 + 8 = - k

4 = -k

Therefore k = -4.

Answer 2

Step-by-step explanation:

So x-2 is a factor of x3 - 3x2 + 4x +k. So x-2 = 0. Hence x = 2. Therefore k = -4.