Final answer:
To multiply the polynomial 3x^2 + x + 2 by the monomial -3x, distribute -3x to each term to get -9x^3 - 3x^2 - 6x.
Step-by-step explanation:
To multiply the polynomial 3x2 + 2x + 2 - x by the monomial -3x, we need to distribute the monomial to each term of the polynomial.
First, we simplify the polynomial: 3x2 + 2x + 2 - x becomes 3x2 + x + 2 because 2x - x equals x.
Now, we multiply each term of the simplified polynomial by -3x:
- -3x * 3x2 = -9x3
- -3x * x = -3x2
- -3x * 2 = -6x
Combine these results to get the final expression: -9x3 - 3x2 - 6x.