Final answer:
To factor out the greatest polynomial from 12g⁵+12g⁴, the greatest common factor is identified as 12g⁴, resulting in a simplified expression: 12g⁴(g + 1).
Step-by-step explanation:
To factor out the greatest polynomial from the expression 12g⁵+12g⁴, we need to identify the largest monomial that is a factor of both terms. Looking at the coefficients, we see that they both have a 12, and for the variables, they both have a g raised to at least the 4th power. Therefore, the greatest common factor (GCF) is 12g⁴.
We can rewrite the original expression by factoring out 12g⁴:
12g⁵ + 12g⁴ = 12g⁴(g + 1).
By factoring out the GCF, we have expressed the original expression in a simplified form where g + 1 is the remaining factor.