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.

Answer

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Answer

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

Steps

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.