Final answer:
The factors of the given expression 4x³ + 9x² - x - 6 are (x² - 1) and (4x + 9), which include options a, b, c, and e.
Step-by-step explanation:
The given expression is 4x³ + 9x² - x - 6. We need to determine which binomial expressions are factors of this expression.
To do this, we can factor the given expression by grouping:
4x³ + 9x² - x - 6 = (4x³ + 9x²) + (- x - 6)
= x²(4x + 9) - 1(4x + 9)
= (x² - 1)(4x + 9)
So, the factors of the given expression are (x² - 1) and (4x + 9).
Among the given options, (x - 1) and (x + 1) are factors of (x² - 1), and (x + 2) and (x - 2) are factors of (4x + 9).
Therefore, the correct factors of the given expression are:
- a. x - 1
- b. x + 1
- c. x + 2
- e. x - 2