Final answer:
To factor the polynomial 4x⁹ + 6x³, we determine the GCF, which is x², and factor it out to obtain x²(4x⁷ + 6x).
Step-by-step explanation:
The student has asked to factor a polynomial using the greatest common factor (GCF). The given polynomial is 4x⁹ + 3² · 2x.
To factor this polynomial, we first identify the GCF. Both terms have an 'x' raised to a power and coefficients that can be divided by 1.
However, since we are looking for the greatest such factor, we notice that 'x' is the factor that appears in all terms to at least the smallest power seen, which is x². So we take x² out:
x²(4x⁷ + 3x · 2)
Further simplifying by multiplying 3x and 2 gives us:
x²(4x⁷ + 6x)
Now, we have our polynomial factored using the GCF.