The value of in given factor form of polynomial is value of k=1.
The given polynomial is,
\(6 x^{3} + 4 x^{2} - 6 x - 4 = 2 ( x + k )(x-k) ( 3 x + 2 )\)
We have to find the value of k
So
\(6 x^{3} + 4 x^{2} - 6 x - 4\)
What is the common factor in above polynomial
2
So factor out 2 we get,
\(= 2 (3x^2+2x^2-3x-2)\\\)
\(= 2 (x^2(3x+2)-(3x+2)\)
\(=2(x^2-1)(3x-2)\\=2(x+1)(x-1)(3x-2)\)
Compare above with the given factor form of polynomial we get,
k=1
Therefore we get the value of k=1
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