Question

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)

Answer 1

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

Explanation:

Answer 2

Option D.

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.