Question

Given the polynomial 6x^3 + 4x^2 - 6x - 4, what is the value of the coefficient 'k' in the factored form?

6x^3 + 4x^2 - 6x - 4 = 2(x + k)(x - k)(3x + 2)

k= ____________

Answer 1

Let 2(x + k)(x - k)(3x + 2) =0
so (3x + 2) =0 i.e. x= -2/3
But (x + k)=0 or (x - k) =0
so x=-k or x=k
or k=-x or k=x
so k= -(-2/3) or k = -2/3
i.e. k= 2/3 or k=-2/3

Answer 2

Everybody agree?

Answer 3

The above answer is incorrect.
6x^3 + 4x^2 - 6x - 4 = 2(x + k)(x - k)(3x + 2) = (2x + 2k)(3x^2 + (2 - 3k)x - 2k) = 6x^3 + (4 - 6k)x^2 - 4kx + 6kx^2 + (4k - 6k^2)x - 4k^2 = 6x^3 + (4 - 6k + 6k)x^2 + (-4k + 4k - 6k^2)x - 4k^2 = 6x^3 + 4x^2 - 6k^2x - 4k^2
Comparing the constants:
-4 = -4k^2
k^2 = 1
k = 1 or k -1

Answer 4

so either one would be correct yea? 1 or -1? wouldn't matter?