Final answer:
The product of 3x⁵ and the trinomial (2x²+4x+1) is found by multiplying each term inside the parentheses by 3x⁵, which yields the expression 6x⁷ + 12x⁶ + 3x⁵, corresponding to option C.
Step-by-step explanation:
The product of 3x⁵ and (2x²+4x+1) is determined by using the distributive property, also known as the foil method when dealing with binomials. In this case, each term inside the parentheses is multiplied by 3x⁵.
The step-by-step calculation is as follows:
- Multiply 3x⁵ by 2x². This results in 6x⁷.
- Multiply 3x⁵ by 4x. This results in 12x⁶.
- Finally, multiply 3x⁵ by 1. This results in 3x⁵.
Combining these results, we get the final expression: 6x⁷ + 12x⁶ + 3x⁵, which matches option C in the provided choices.