Math
posted by Sarah .
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^512^4+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^54x^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^24x+6)
At this point you can struggle to find the factors, or note first that the discriminant is
1624 = 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).