Question

is \\((x - 2)\\) a factor of \\(-3x^3 + 7x^2 - 2x\\)?

no, it is a not factor.
yes, it is a factor.

Explanation:

Step 1: Define the polynomial function

$$P(x) = -3x^3 + 7x^2 - 2x$$

Step 2: Apply the Factor Theorem

$$P(2) = -3(2)^3 + 7(2)^2 - 2(2)$$

Step 3: Evaluate the expression

$$P(2) = -3(8) + 7(4) - 4 = -24 + 28 - 4 = 0$$

Answer:

Yes, it is a factor.