Question

Factor out the great common factor from the terms of the polynomial 6x^3 - 12x^2 + 18x.

Also I need it step by step please.

Answer 1

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

Explanation:

By looking at these terms, we can realize that they all have a term to do with x and are divisible by 6. So, we have our GCF, which is 6x. Now, to factor out 6x, we have to divide every term by 6x; they will all divide without a remainder because we already established they were all divisible by 6x.

So, we get the division(for each term separately):

6x^3/6x - we can cancel out 6x from the numerator and denominator to get: x^2

-12x^2/6x - we can cancel out 6x from the numerator and denominator to get: -2x

-18x/6x - we can cancel out 6x from the numerator and denominator to get:

3

When we put this together we get:

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

This is the final answer