Final answer:
To find the completely factored form of the polynomial, first distribute and combine like terms, then factor out common factors in each term.
Step-by-step explanation:
The completely factored form of the polynomial is sought in this mathematics question. By combining like terms, we start simplifying the given expression 4x³ + 12x² + 5x + 154x²(x + 3) + 5(x + 3). First, we distribute the 154x² and the 5 into the parentheses:
- 154x² * x = 154x³
- 154x² * 3 = 462x²
- 5 * x = 5x
- 5 * 3 = 15
Adding these to the original polynomial, we have: 4x³ + 12x² + 5x + 154x³ + 462x² + 5x + 15. Next, we combine like terms:
- 4x³ + 154x³ = 158x³
- 12x² + 462x² = 474x²
- 5x + 5x = 10x
We get: 158x³ + 474x² + 10x + 15. Now, to factor, we look for common factors in each term. All terms are divisible by 2, so we factor out a 2:
2(79x³ + 237x² + 5x + 15/2)
Unfortunately, there appears to be a typo or some confusion with the initial expression provided by the student. It is not clear if additional factoring can be done or if the expression was intended to be different. Further clarification from the student would be necessary to proceed.