Factor 2x3 – 12x2 + 16x.A.2(x2 + 2)(x – 4)B.2x(x + 2)(x – 4)C.2x(x – 2)(x – 4)D.2(x2 – 2)(x – 4)

The first step in factoring the expression 2x^3 - 12x^2 + 16x is to look for the greatest common factor (GCF). The GCF of the terms 2x^3, -12x^2, and 16x is 2x.

So, we factor out the GCF from each term:

2x^3 ÷ 2x = x^2 -12x^2 ÷ 2x = -6x 16x ÷ 2x = 8

This gives us 2x(x^2 - 6x + 8).

The next step is to factor the quadratic expression x^2 - 6x + 8. We look for two numbers that multiply to 8 and add to -6. The numbers -2 and -4 meet these criteria.

So, x^2 - 6x + 8 factors to (x - 2)(x - 4).

Putting it all together, the factored form of the expression 2x^3 - 12x^2 + 16x is 2x(x - 2)(x - 4).

So, the correct answer is C. 2x(x - 2)(x - 4).