Factor

6x^6-15x^3+21x^2

To factor the expression 6x^6 - 15x^3 + 21x^2, we can first look for the greatest common factor (GCF) among the terms. In this case, the GCF is 3x^2. By factoring out the GCF, the expression becomes:

3x^2(2x^4 - 5x + 7).

Now, let's focus on factoring the remaining expression within the parentheses (2x^4 - 5x + 7). Unfortunately, this expression cannot be factored further using simple integer coefficients. Therefore, we can conclude that the factored form of the original expression 6x^6 - 15x^3 + 21x^2 is:

3x^2(2x^4 - 5x + 7).