Final answer:
To factor out the GCF of the polynomial 12m³-8m²+16m+8, first determine the GCF (4m in this case) and divide each term by the GCF. The factored form is 4m(3m² - 2m + 4 + 2/m).
Step-by-step explanation:
To factor a monomial from the polynomial 12m³-8m²+16m+8, first identify the Greatest Common Factor (GCF), which is the largest monomial that divides each term of the polynomial without leaving a remainder. In this case, the GCF is 4m since it is the highest power of m that can divide each term, and 4 is a common factor of all the numerical coefficients.
We can factor out 4m from each term of the polynomial:
12m³ can be factored as 4m × 3m².
8m² can be factored as 4m × 2m.
16m can be factored as 4m × 4.
8 can be factored as 4m × 2/m (we divide the constant by m).
When we factor out 4m, we get:
4m(3m² - 2m + 4 + 2/m)