Question

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

Answer 1

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.

Answer 2

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).