Answer: (x - 2)(x² + 4)
Step-by-step explanation: If you're asked to factor this problem, you'll soon realize that there is no greatest common factor for all four of these terms and it's not set up as a trinomial that can be factored as the product of two binomials.
So we need to figure out a new way of factoring this problem.
The way you do it is by grouping terms together.
If we group the first two terms together, x³ - 2x², and the last two terms together, +4x - 8, we can factor out a greatest common factor from our first group of terms and a greatest common factor for our last group of terms.
The greatest common factor for x³ - 2x² is x².
That leaves you with x - 2 inside the parentheses.
The greatest common factor for +4x - 8 is +4.
That leaves you with x - 2 also in the parentheses.
Since there is an x - 2 in each of these two terms, it factors out so we have x -2 times what's left inside the parentheses which is x² + 4 and that's your answer.
(X - 2)(x² + 4)