x^2-16x+63 Select the correct choice below and, if necessary,fill in the answer box within your choice. A. x^2-16x+63=square B. The polynomial is prime.

To determine whether the polynomial $x^2 - 16x + 63$ can be factored, we need to check if there are two numbers that multiply to 63 and add up to -16.

The polynomial is in the form of a quadratic expression $ax^2 + bx + c$, where $a = 1$, $b = -16$, and $c = 63$.

We are looking for two numbers whose product is $c = 63$ and whose sum is $b = -16$.

Let's list the pairs of factors of 63:
- $1 \times 63$
- $3 \times 21$
- $7 \times 9$

Now, let's consider their negative counterparts since we need a sum of -16:
- $(-1) \times (-63)$
- $(-3) \times (-21)$
- $(-7) \times (-9)$

Among these, $-7$ and $-9$ add up to $-16$ and multiply to $63$.

Thus, the polynomial can be factored as:
$$x^2 - 16x + 63 = (x - 7)(x - 9)$$

Therefore, the correct choice is:

A. $x^{2}-16 x+63= (x - 7)(x - 9)$