Final answer:
To factor the polynomial 8x + 16x² + 80x³, the GCF is 8x. Therefore, it is factored as 8x(1 + 2x + 10x²).
Step-by-step explanation:
Factoring the Polynomial by Using the Greatest Common Factor (GCF)
To factor the polynomial 8x + 16x² + 80x³, we first need to find the GCF of the coefficients and the smallest power of x that is common to all three terms. The GCF of the coefficients (8, 16, and 80) is 8, and the smallest power of x common to all terms is x. Therefore, the GCF is 8x.
Now we can factor out the GCF from each term of the polynomial:
8x(1) + 16x²(8x) + 80x³(8x) = 8x(1 + 2x + 10x²)
So the polynomial 8x + 16x² + 80x³ factored by using the Greatest Common Factor is 8x(1 + 2x + 10x²).