I really want to understand factoring, and I have a problem and the answer but I don't understand the steps to getting an answer. 3x^5-12^4+18x^3

The first thing to do, to make life simpler, is to factor out any constant, so you are working with smaller numbers. That gives you

3(x^5-4x^4+6x^3)

Now note that all the powers of x are at least 3, meaning you can factor out an x^3:

3x^3(x^2-4x+6)

At this point you can struggle to find the factors, or note first that the discriminant is

16-24 = -8

which is negative, so you know that you cannot factor it any further, using real numbers.

3x^5 - 12x^4 + 18x^3.

1. Locate the smallest constant which is
3. If 3 will divide into the other constants with no remainder, factor out 3.

2. Factor out the variable with the smallest exponent which is x^3.
We have factored out 3x^3.

3. To determine what goes inside of the parenthesis, divide each term by 3x^3
and get:

3x^3(x^2 - 4x + 6).

To factor the expression 3x^5 - 12x^4 + 18x^3, we can start by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 3x^3 since it is the largest factor that can be divided evenly from each term.

Step 1: Factor out the GCF, which is 3x^3:
3x^3(x^2) - 3x^3(4x) + 3x^3(6)

Step 2: Simplify each term:
3x^5 - 12x^4 + 18x^3 = 3x^3(x^2 - 4x + 6)

Now we have factored the original expression as 3x^3(x^2 - 4x + 6).

Note: Factoring further may require techniques such as using the quadratic formula or factoring methods specific to quadratic trinomials. However, since the expression in your question is already in its factored form, we don't need to go further.