Final answer:
The product of the polynomials 3c - 8 and -6t + 12 involves multiplying each term of one polynomial by each term of the other. However, none of the answer choices strictly match the multiplication result, suggesting a possible error in the question.
Step-by-step explanation:
To find the product of the polynomials 3c — 8 and —6t + 12, we apply the distributive property, which involves multiplying each term of the first polynomial by each term of the second polynomial. Here are the steps:
- Multiply 3c by —6t: (3c)(-6t) = -18ct.
- Multiply 3c by +12: (3c)(12) = 36c.
- Multiply —8 by —6t: (-8)(-6t) = 48t.
- Multiply —8 by 12: (-8)(12) = -96.
However, since the original question mentions c and t but does not mention any term with just t such as 48t, we may consider that there has been a typo in the original expression and the correct term should have a c instead of a t. If this is the case, then the multiplication of —8 by —6t should result in —48tc. This multiplication, however, would not affect our answer since it combines variables that were not present in the original polynomials.
After adding the term with similar variables, which is 36c - 48tc, we have the final product of -18ct + 36c. But again, as this involves variables not specified in the options provided, we acknowledge a potential misunderstanding or typo in the provided problem. If you refer to only the terms with common variables, -18ct is the correct product term for 3c and -6t.
It seems there may be an error in the question as none of the options provided completely match the expected result of the polynomial multiplication.