Question

Factor out the GCF of the following polynomial 6m^3n^2-12m^2n^3+18mn

Answer 1

The GCF of the polynomial 6m^3n^2-12m^2n^3+18mn is 6mn. The factored form of the polynomial is 6mn(m^2n - 2mn^2 + 3).

Step-by-step explanation:

Factoring out the GCF (Greatest Common Factor)

To factor out the GCF of the polynomial 6m^3n^2-12m^2n^3+18mn, you need to first identify the greatest common factor of the terms. The GCF of these terms is 6mn, as it is the highest number that can divide each term and 'mn' is the highest power of the variables common to all three terms.

Therefore, we divide each term by 6mn:

• 6m^3n^2 divided by 6mn gives us m^2n.
• 12m^2n^3 divided by 6mn gives us -2mn^2.
• 18mn divided by 6mn gives us 3.

The factored form of the polynomial is thus 6mn(m^2n - 2mn^2 + 3).