Final answer:
The possible factors of the polynomial can be found using polynomial long division or synthetic division.
Step-by-step explanation:
The possible factors of the expression 5x³ + 6x² + 4x - 5640 can be found by performing polynomial long division or by using synthetic division. Both methods will yield the same result. I will demonstrate how to use synthetic division to find the factors:
- Set up the synthetic division grid with the given polynomial and try dividing it by the potential factor.
- Start by bringing down the coefficient of the highest degree term (5 in this case).
- Multiply the potential factor by the result you obtained in the previous step, then write the product in the next column.
- Add the product to the next coefficient (6 in this case), and continue this process until you reach the last coefficient (-5640 in this case).
By performing the above steps, you will be able to find the factors of the given polynomial.