Final answer:
The polynomial is written in standard form as -6x^3 + 5x^2 + 6x, with a degree of 3 and consisting of 3 terms. No option provided matches this correct classification.
Step-by-step explanation:
To write the polynomial in standard form and classify it by degree and number of terms, we first need to combine like terms in the expression 12x2 - 4x3 - 7x2 + 6x - 2x3:
- Combine like terms by adding coefficients of the same degree: -4x3 - 2x3 gives us -6x3, and 12x2 - 7x2 gives us 5x2.
- After combining, the polynomial is -6x3 + 5x2 + 6x.
- Put the terms in descending order of degree to get the standard form. As there are no other like terms to combine, the polynomial is already in standard form: -6x3 + 5x2 + 6x.
The polynomial has a highest degree of 3, which classifies it as a cubic polynomial. It consists of 3 terms.
Therefore, the correct classification for the polynomial is degree 3, 3 terms.