Answer: (2x + 1)(x - 1)
Explanation:
We can use polynomial long division or synthetic division to find the other factor of the polynomial. Alternatively, we can use the fact that if (x - 2) is a factor of the polynomial 2x^3 - 3x^2 - 3x + 2, then (2 - x) is also a factor of the polynomial.
We can use synthetic division to divide the polynomial by (2 - x) and obtain the quotient polynomial:
2 -3 -3 2
2-x | 2 -3 -3 2
- 4 14 -22
2 -7 11 0
Therefore, the other factor of the polynomial is 2x^2 - 7x + 11. We can factor this quadratic expression as (2x + 1)(x - 1).
Thus, the factorization of the polynomial 2x^3 - 3x^2 - 3x + 2 is:
2x^3 - 3x^2 - 3x + 2 = (x - 2)(2x + 1)(x - 1)