Final answer:
The complete factorization of 6x3 + 12x2 is done by factoring out the greatest common factor, which is 6x2, resulting in 6x2(x + 2). This expression cannot be factored further since x + 2 is a linear polynomial with no additional common factors.
Step-by-step explanation:
The complete factorization of the expression 6x3 + 12x2 requires factoring out the greatest common factor (GCF) from both terms. The GCF is the largest expression that is a factor of both terms. In this case, since both terms contain the variable x and also a multiple of 6, we can factor out 6x2 (which is the GCF).
Here's a step-by-step process to factor the expression:
-
-
-
6x3 + 12x2 = 6x2(x + 2)
This expression cannot be factored further as x + 2 is a linear polynomial and does not have any common factors with the coefficient.