Multiple Choice 10 points n^2-14n+45 (n+4)(n-4) (n-5)(n-9) (n-5)(n+9) (n+2)(n+3)

To factor the quadratic expression $n^2 - 14n + 45$, we need to find two numbers that multiply to 45 and add up to -14.<br /><br />Let's analyze the given options:<br /><br />1. $(n+4)(n-4)$: This expands to $n^2 - 16$, which is not the same as $n^2 - 14n + 45$.<br />2. $(n-5)(n-9)$: This expands to $n^2 - 14n + 45$, which matches the given expression.<br />3. $(n-5)(n+9)$: This expands to $n^2 + 4n - 45$, which is not the same as $n^2 - 14n + 45$.<br />4. $(n+2)(n+3)$: This expands to $n^2 + 5n + 6$, which is not the same as $n^2 - 14n + 45$.<br /><br />Therefore, the correct answer is:<br />$(n-5)(n-9)$