Question 1, R.5.51 Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime. \[ x^{2}-2 x-63 \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $x^{2}-2 x-63=\square$ B. The polynomial is prime.

Step 1 ：Given polynomial is \(x^{2}-2x-63\).

Step 2 ：We need to find two numbers that multiply to -63 and add to -2.

Step 3 ：The numbers -9 and 7 satisfy these conditions because \((-9) * 7 = -63\) and \(-9 + 7 = -2\).

Step 4 ：So, we can write the polynomial as \(x^{2}-2x-63 = (x - 9)(x + 7)\).

Step 5 ：\(\boxed{x^{2}-2x-63 = (x - 9)(x + 7)}\) is the final answer.