Final answer:
The GCF of the expression 9x^4 + 3x^3 + 12x^2 is 3x^2, which allows us to factor the polynomial as 3x^2(3x^2 + x + 4).
Step-by-step explanation:
The Greatest Common Factor (GCF) of the expression 9x4 + 3x3 + 12x2 is found by identifying the largest factor that divides each term of the polynomial without leaving a remainder. To find the GCF of this expression, we first factor each coefficient (9, 3, 12) and the variables:
- 9x4 = 3² ⋅ x4
- 3x3 = 3 ⋅ x3
- 12x2 = 3 ⋅ 22 ⋅ x2
The common factor present in all three terms is 3x2. So, the GCF is 3x2. We can rewrite the polynomial in factored form by factoring out the GCF:
3x2(3x2 + x + 4)