Final answer:
The polynomial 2u³ + 3u² + 14u + 21 can be factored by grouping. After grouping and factoring out the greatest common factors, it becomes (u² + 7)(2u + 3).
Step-by-step explanation:
The question asks to factor by grouping the polynomial 2u³ + 3u² + 14u + 21. To do this, let's begin by breaking the polynomial into groups that have common factors:
(2u³ + 3u²) + (14u + 21)
Now, from each group, we factor out the greatest common factor (GCF). In the first group, the GCF is u², and in the second group, it is 7:
u²(2u + 3) + 7(2u + 3)
Now, we can see that both groups have a common binomial factor (2u + 3). So we factor out this common binomial:
(u² + 7)(2u + 3)
Thus, the factored form of 2u³ + 3u² + 14u + 21 is (u² + 7)(2u + 3).