Answer:
(x^2 - 2)(x - 4).
Explanation:
To factor the expression x^3 - 3x^2 + 2x - 8, we can use a combination of grouping and factoring by grouping.
First, we can group the first two terms and the last two terms together:x^3 - 3x^2 + 2x - 8 = (x^3 - 3x^2) + (2x - 8)
Next, we can factor out x^2 from the first group and 2 from the second group:x^3 - 3x^2 + 2x - 8 = x^2(x - 3) + 2(x - 4)
Now, we can see that both terms have a common factor of (x - 4), so we can factor that out:x^3 - 3x^2 + 2x - 8 = (x^2 - 2)(x - 4)
Therefore, the factored form of the expression x^3 - 3x^2 + 2x - 8 is (x^2 - 2)(x - 4).