J) Simplify.Write your answer using whole numbers and variables. (n^2-12n+32)/(n-8) square

To simplify the expression \(\frac{n^2 - 12n + 32}{n - 8}\), we need to factor the numerator and see if it has a common factor with the denominator.<br /><br />First, let's factor the quadratic expression in the numerator:<br />\[ n^2 - 12n + 32 \]<br /><br />We are looking for two numbers that multiply to 32 and add up to -12. These numbers are -4 and -8 because:<br />\[ (-4) \times (-8) = 32 \]<br />\[ (-4) + (-8) = -12 \]<br /><br />So, we can factor the quadratic as:<br />\[ n^2 - 12n + 32 = (n - 4)(n - 8) \]<br /><br />Now, substitute this factored form back into the original expression:<br />\[ \frac{(n - 4)(n - 8)}{n - 8} \]<br /><br />Since \(n - 8\) is a common factor in both the numerator and the denominator, we can cancel it out (assuming \(n \neq 8\) to avoid division by zero):<br />\[ \frac{(n - 4)(n - 8)}{n - 8} = n - 4 \]<br /><br />Therefore, the simplified form of the given expression is:<br />\[ \boxed{n - 4} \]