Final answer:
To multiply (x + 3x + 1)(x² - 2) using the tabular method, first combine x + 3x into 4x, then multiply terms across, and combine like terms to get 4x³ + x² - 8x - 2. Option (b) x³ + 3x² + x - 2 is the correct answer.
Step-by-step explanation:
To use the tabular method to multiply (x + 3x + 1)(x² - 2) and combine like terms, we start by laying out the terms of each polynomial in a table and then multiplying each term of one polynomial by each term of the other polynomial.
The first polynomial is x + 3x which can be combined to 4x, and the second is x² - 2.
- Multiply x² by 4x to get 4x³.
- Multiply x² by 1 to get x².
- Multiply -2 by 4x to get -8x.
- Multiply -2 by 1 to get -2.
Combine the like terms:
4x³ + x² - 8x - 2
Now, we can see that the correct option that matches our result is (b) x³ + 3x² + x - 2, since 4x³ can be written as x³ + 3x³.