Question

Compute $\frac{x^8+12x^4+36}{x^4+6}$ when $x=5$.

Answer 1

Note that x^8 + 12x^4 + 36 = (x^4 + 6)^2. Thus the expression equals x^4 + 6. For x = 5, this is 5^4 + 6 = 625 + 6 = 631.