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Given the polynomial 2x3 + 18x2 − 18x − 162, what is the value of the coefficient 'k' in the factored form?

2x3 + 18x2 − 18x − 162 = 2(x + k)(x − k)(x + 9)

k= ____________

Respuesta :

celestialflames15

Your Answer:

k = 3

Hope this helps y'all :)

Answer:

Step-by-step explanation:

Alright, lets get started.

[tex]2x^3 + 18x^2 -18x -162 = 2(x+k)(x-k)(x+9)[/tex]

[tex]2(x+k)(x-k)(x+9) =2x^3 + 18x^2 -18x -162[/tex]

[tex]2(x^2-k^2)(x+9)=2x^3 + 18x^2 -18x -162[/tex]

[tex]2(x^3+9x^2-k^2 x+9k^2)=2x^3 + 18x^2 -18x -162[/tex]

[tex]2x^3 + 18x^2 -2k^2x+18k^2= 2x^3 + 18x^2 -18x -162[/tex]

comparing both sides

[tex]2k^2 =18[/tex]

[tex]k^2=9[/tex]

[tex]k=3[/tex]

hence answer is k = 3(plus/minus)   :  Answer

Hope it will help :)

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