FACTOR THE FOLLOWING EXPRESSION COMPLETELY:

-6X^3-20X^2+16X

-6x^3 - 20x^2 + 16x

-2x(3x^2 + 10x - 8)
-2x(3x-2)(x+4)

To factor the expression completely, we need to identify the greatest common factor (GCF) and then use factoring techniques to rewrite each term.

Step 1: Find the GCF
The GCF of -6x^3, -20x^2, and 16x is 2x, as it is the largest common factor that can divide into all three terms.

Step 2: Factor out the GCF
We'll factor out 2x from each term:
-6x^3 / 2x = -3x^2
-20x^2 / 2x = -10x
16x / 2x = 8

Now, we can rewrite the expression as:
2x(-3x^2 - 10x + 8)

Step 3: Factoring the Quadratic Trinomial Inside
Now, we need to factor the quadratic trinomial (-3x^2 - 10x + 8). Since the coefficient of x^2 is negative, we will look for two numbers that multiply to give the product of the quadratic term coefficient (-3) and the constant term (8) and add up to the coefficient of the linear term (-10).

To factor the quadratic trinomial, we can rewrite it as a product of two binomials:
(-3x^2 - 10x + 8) = (ax + b)(cx + d)

Since the coefficient of x^2 is -3, and the constant term is 8, the possible combinations for a, b, c, and d are as follows:
ac = -3
bd = 8
ad + bc = -10

We need to find two numbers that satisfy both equations. After some trial and error, we find that the correct combination is:
a = -1
b = 2
c = 3
d = -4

Therefore, we can rewrite the quadratic trinomial as:
(-3x^2 - 10x + 8) = (-x + 2)(3x - 4)

Putting it all together, we have:
-6x^3 - 20x^2 + 16x = 2x(-x + 2)(3x - 4)

The expression is factored completely as 2x(-x + 2)(3x - 4).