To determine the factors of the expression 12x3 + 2x2 + 18x3 by grouping, we first rearrange the terms:
12x3 + 18x3 + 2x2
Next, we can group the first two terms and the last term:
(12x3 + 18x3) + (2x2)
Now, factor out the common factors from each group:
6x3(2 + 3) + 2x2
This simplifies to:
6x3 imes 5 + 2x2
Next, we can see that the entire expression can also share a common factor of 2x2. Factoring out 2x2 from the expression:
2x2(3x + 9x + 1) = 2x2(12x + 1)
Thus, the final factors of the expression are: 2x2 and (12x + 1).