To factor the expression 8x³ + 2x² + 12x by grouping, we start by grouping the terms in pairs. Let’s rewrite the expression:
(8x³ + 2x²) + (12x)
Now we’ll look at each group separately:
1. In the first group, 8x³ + 2x², we can factor out the common factor 2x²:
2x²(4x + 1)
2. In the second group, we only have 12x, which can be rewritten as 12x(1), but we need to match the format. Notice that we can factor out 4x from this group to achieve uniformity:
4x(3)
Thus our expression looks a bit different; we might rearrange it to resemble our first factorization:
(2x²(4x + 1) + 4x(3))
Now, we can see that we need to factor out the common term since (4x + 1) does not appear in the second grouping. Instead, let’s go back and combine results:
Let’s redo it for clearer sense:
Begin with Full expression: 8x³ + 2x² + 12x
Factor out the greatest common factor from all terms:
2x (4x² + x + 6)
The resulting factors provide the simplified expression:
2x(4x² + x + 6)
Thus, the final factored expression for 8x³ + 2x² + 12x after proper grouping and factorization is:
2x(4x² + x + 6)