If x - 3 is a factor of P (x) = x^3-7x^2+15-9, which of the following represents the complete factorization for P (x)

A. (x-3) (x+3) (x+1)

B. (x-3) (x+4) (x+1)

C. (x-3) (x+3) (x-1)

D. (x-3) (x-3) (x-1)

Option D.

Step-by-step explanation:

Given that (x-3) is a factor of P (x) = x^3-7x^2+15x-9. If we divide the P (x) by (x-3) we will get a second grade polynomial, which is easier to factorize.

Dividing x^3-7x^2+15x-9 by (x-3), the answer is: x^2 - 4x + 3 with a remainder of zero.

Now, to factorize x^2-4x+3 we just need to find two numbers that equal - 4 when added and 3 when multiplied. These two numbers are - 1 and - 3.

So the complete factorization of P (x) is: (x-3) (x-1) (x-3)

Which is option D.