To determine the completely factored form of the expression 8x2 + 50, we will first look for the greatest common factor (GCF) of the terms in the expression. The coefficients are 8 and 50, and their GCF is 2.
Now, let’s factor out the GCF:
8x2 + 50 = 2(4x2 + 25)
Next, we see that 4x2 + 25 is a sum of squares. Sum of squares cannot be factored into real numbers using standard algebraic methods, as it does not equal zero. However, if we are considering complex numbers, we can factor it further:
4x2 + 25 = (2x + 5i)(2x - 5i)
Putting this back together, we have:
8x2 + 50 = 2(2x + 5i)(2x - 5i)
Thus, the completely factored form of 8x2 + 50 is:
2(2x + 5i)(2x - 5i)
To summarize:
- Factored out the GCF: 2
- Recognized the sum of squares and factored into complex numbers
- The fully factored expression is 2(2x + 5i)(2x – 5i)
This expression represents the completely factored form of the given polynomial involving a complex factorization.