Final answer:
The GCF of the polynomial 3x⁴-24x² is 3x², and the factored form is 3x²(x² - 8).
Step-by-step explanation:
To find the GCF and factor out the polynomial 3x⁴-24x², we first need to look for the highest common factor of the coefficients (numbers) and the variables (powers of x). The coefficients of 3 and 24 have a common factor of 3. The variables have a common factor of x². So, the GCF is 3x². Now, we can factor out the GCF from the polynomial:
3x⁴ - 24x² = 3x²(x² - 8)
Therefore, the GCF of the polynomial is 3x² and the factored form of the polynomial is 3x²(x² - 8).