Answer :

the answer choice is d because the the greatest exponent is 4 but you cant take 4 exponents out of 2 . Both numbers are divisible by [tex]2 x^{2} [/tex] which would make the answer [tex]13+17 x^{2} [/tex] 
26x²: 13 · 2 · x · x
34x⁴: 17 · 2 · x · x

GCF: 2x²

26x² + 34⁴
2x²(13) + 2x²(17x²)
2x²(13 + 17x²)

The answer is equal to D.