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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= ____________

Answer :

kudzordzifrancis

Answer:

[tex]k=3[/tex]

Step-by-step explanation:

Let

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

We factor 2 to obtain;

[tex]f(x)=2(x^3+9x^2-9x-81)[/tex]

We factor the polynomial within the parenthesis by grouping.

[tex]f(x)=2(x^2(x+9)-9(x+9)[/tex]

[tex]f(x)=2(x^2-9)(x+9)[/tex]

[tex]f(x)=2(x^2-3^2)(x+9)[/tex]

We apply difference of two squares on the second factor: [tex]x^2-3^2=(x-3)(x+3)[/tex]

[tex]f(x)=2(x+3)(x-3)(x+9)[/tex]

We now compare to;

[tex]f(x)=2(x+k)(x-k)(x+9)[/tex]

It is now obvious that [tex]k=3[/tex]

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