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Hallo!

Step-by-step explanation:

x^3 - 9x + 2x^2 - 18

It's a bit odd to write the polynomial this way.  Let's sort by degree.

x^3 + 2x^2 -9x - 18

That's less confusing.  Let's check Jay's factorization:

(x+2) (x^2 - 9) = x^3 + 2x^2 - 9x - 18

Seems correct.  

(a) Jay's problem is that he still has more factoring to do.  The second factor he has is the difference of two squares:

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

(b)

Let's factor f(x) = x^3 - 9x + 2x^2 - 18

Playing around with some small numbers we find

f(-2) = 0

so (x + 2) is a factor.  

x^3 + 2x^2 -9x - 18

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

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

= (x+3)(x-3)(x+2)