Final answer:
The sum of 34 plus 51 using the greatest common factor and the distributive property is 17(5), as both numbers are divisible by 17 and then factored out.
Step-by-step explanation:
To find the sum of 34 plus 51 using the greatest common factor (GCF) and the distributive property, we first need to determine the GCF of 34 and 51. Both numbers are divisible by 17, so the GCF is 17. Applying the distributive property, we divide each number by the GCF and factor it out:
34 + 51 = 17(2) + 17(3) = 17(2 + 3) = 17(5)
Therefore, the sum of 34 plus 51, factored using the greatest common factor and the distributive property, is 17(5), which corresponds to option c) 17(5).