Will mark
the polynomial p(x)=x^3-6x^2+6x-23 can be rewritten as p(x)=(x^2+6)(x-6)+13 . which expression is a factor of p(x)?
a. 13
b. x-6
c. none of these
d. x^2+6

None of these.

Step-by-step explanation:

Let's assume we are trying to figure out if (x-6) is a factor. We got the quotient (x^2+6) and the remainder 13 according to the problem.  So we know (x-6) is not a factor because the remainder wasn't zero.

Let's assume we are trying to figure out if (x^2+6) is a factor.  The quotient is (x-6) and the remainder is 13 according to the problem.  So we know (x^2+6) is not a factor because the remainder wasn't zero.

In order for 13 to be a factor of P, all the terms of P must be divisible by 13.  That just means you can reduce it to a form that is not a fraction.

If we look at the first term x^3 and we divide it by 13 we get we cannot reduce it so it is not a fraction so 13 is not a factor of P

None of these is the right option.

C. None of these

Step-by-step explanation:

The polynomial P(x)=x^3-6x^2+6x-23 can be rewritten as P(x)=(x^2+6)(x-6)+13.

The following expressions are given as possible answer choices:

13

x-6

x^2+6

However, none of these would be the correct answer.