Question

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 1

`k=3`

Explanation:

Let

`f(x)=2x^3+18x^2-18x-162`

We factor 2 to obtain;

`f(x)=2(x^3+9x^2-9x-81)`

We factor the polynomial within the parenthesis by grouping.

`f(x)=2(x^2(x+9)-9(x+9)`

`f(x)=2(x^2-9)(x+9)`

`f(x)=2(x^2-3^2)(x+9)`

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

`f(x)=2(x+3)(x-3)(x+9)`

We now compare to;

`f(x)=2(x+k)(x-k)(x+9)`

It is now obvious that
`k=3`