To factor the expression 7x³ + 21x² + 3x + 9 by grouping, we start by grouping the terms into two pairs.
We can group the first two terms together and the last two terms together:
(7x³ + 21x²) + (3x + 9)
Now, we factor out the greatest common factor from each group:
From the first group (7x³ + 21x²), we can factor out 7x²:
7x²(x + 3)
From the second group (3x + 9), we can factor out 3:
3(x + 3)
Now, we can rewrite the expression as:
7x²(x + 3) + 3(x + 3)
Next, we notice that (x + 3) is common in both terms, so we can factor that out:
(x + 3)(7x² + 3)
Thus, the resulting expression after factoring by grouping is:
(x + 3)(7x² + 3)