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Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the constant 'k' in the factored form?

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

k= ____________

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Answer:

Value of k is 1      

Step-by-step explanation:

Given the polynomial [tex]6x^3 + 4x^2 - 6x - 4[/tex]

we have to find the value of k in factored form

[tex]6x^3 + 4x^2 - 6x - 4 = 2(x + k)(x - k)(3x + 2)[/tex]

[tex]6x^3 + 4x^2 - 6x - 4\\\\=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)\\\\=2(x+1)(x-1)(3x-2)[/tex]

Compare above with given factored form, we get

k=1

Hence, value of k is 1