Answer: ![\frac{5x^2-16}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%5E2-16%7D%7B2%7D)
Step-by-step explanation:
Given the following expression:
![\frac{10x^2-32}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B10x%5E2-32%7D%7B4%7D)
Find the Greatest Common Factor (GCF) of the numerator. The steps to do this are:
1. You need to descompose into prime factors:
![10x^2=2*5*x^2\\\\32=2*2*2*2*2=2^5](https://tex.z-dn.net/?f=10x%5E2%3D2%2A5%2Ax%5E2%5C%5C%5C%5C32%3D2%2A2%2A2%2A2%2A2%3D2%5E5)
2. Now you must choose the common ones with the lowest exponents and multiply them. In this case the common one is 2 and its lowest exponent is 1, then:
![GCF=2](https://tex.z-dn.net/?f=GCF%3D2)
Knowing this, you can factor out the Greatest Common Factor (GCF) in the numerator:
![=\frac{2(5x^2-16)}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%285x%5E2-16%29%7D%7B4%7D)
Finally, simplifying, you get:
![=\frac{5x^2-16}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5x%5E2-16%7D%7B2%7D)