To factor the expression 8x² + 50, we can start by recognizing that both terms share a common factor. The greatest common factor (GCF) of 8 and 50 is 2. We can factor out the GCF:
8x² + 50 = 2(4x² + 25)
Next, we look at the expression inside the parentheses, which is 4x² + 25. This is a sum of squares, but it cannot be factored over the real numbers. However, if we consider factoring over the complex numbers, we can express 4x² + 25 as:
4x² + 25 = (2x + 5i)(2x – 5i)
Putting it all together, the completely factored form of the original expression over the complex numbers is:
8x² + 50 = 2(2x + 5i)(2x – 5i)
If we are only considering real numbers, the completely factored form is:
2(4x² + 25)
In summary, we have two answers depending on the context: for real numbers, it is 2(4x² + 25), and for complex numbers, it is 2(2x + 5i)(2x – 5i).