Natasha’s family has advised her not to depend completely on the insurance that her employer provides. Natasha now plans to independently obtain property and casualty insurance, auto insurance, and other insurance related to her personal life. What are the two ways in which she can accomplish her goal?

C. by hiring a local agent or broker who is familiar with her needs

and

E. by registering on the website of a national insurance company

Step-by-step explanation:

Notice that 6 is a factor of all three coefficients and thus can be factored out:

6x^2 -42x-54  =>  6(x^2 - 7x - 9).   x^2 - 7x - 9  does not factor so easily.  Remembering that obtaining roots of a quadratic makes it easy to write out the corresponding factors, let's apply the quadratic formula to x^2 - 7x - 9:

a=1, b = -7, c = -9. Then the discriminant is b^2 - 4ac, or (-7)^2 - 4(1)(-9), or 85.

Thus, the roots are:

      7 plus or minus √85        7 plus or minus 9.220

x = =

                 2                                           2

Let's call these roots "a" and "b."  Then the factors of the quadratic x^2 - 7x - 9 are (x-a) and (x-b), or, in this case, (x-8.11) and (x+1.11).

The original quadratic has three factors:  6, (x-8.11) and (x+1.11).