8) \( j^{2}-16 j+n \)

To factor the expression \( j^{2}-16 j+n \), we can first look at the quadratic part, which is \( j^2 - 16j \). This can be completed to form \( (j - 8)^2 - 64 \). Thus, we rewrite the expression as \( (j - 8)^2 - 64 + n \). The overall factorization will depend on the value of \( n \). If \( n = 64 \), it becomes \( (j - 8)^2 \); if \( n \) differs, it takes a different form. Keep in mind this plays a crucial role in determining the roots of the equation based on the value of \( n \). If you find yourself stuck with a quadratic expression like this, always remember to check for possible completing the square or factoring patterns. Also, double-check your calculations for signs when substituting values, as it's easy to misplace a negative sign!