Why can't x^2+9 be factorised with real numbers?

Answer 1

We can look at the quadratic equation for answers to tricky factoring questions:

x = (–b ± √(b² – 4ac))/2a

x = (0 ± √(0 – 4×1×9))/2

x = ± √(–36)/2

x = ± 6 √(–1)/2

Since we have a negative number within the square root, the answer for x cannot be real and must be imaginary.