Question

Which of the following expressions are factors of 25x³ −75x² −9x+27? There may be more than one correct answer.

Select all correct answers.
A. x² −3x+9
B. x−3
C. x² +6x+9
D. 5x+3
E. x+3
F. 5x−3

Answer 1

To find the factors of the given expression, we can perform long division or synthetic division to check if the options are factors. The correct factors of 25x³ - 75x² - 9x + 27 are B) x - 3, C) x² + 6x + 9, and E) x + 3.

Step-by-step explanation:

In order to determine which of the given expressions are factors of 25x³ - 75x² - 9x + 27, we can use long division or synthetic division.

1. For option A. x² - 3x + 9, performing long division or synthetic division will result in a remainder, indicating that it is not a factor.
2. For option B. x - 3, performing long division or synthetic division will result in a remainder of 0, indicating that it is a factor.
3. For option C. x² + 6x + 9, performing long division or synthetic division will result in a remainder of 0, indicating that it is a factor.
4. For option D. 5x + 3, performing long division or synthetic division will result in a remainder, indicating that it is not a factor.
5. For option E. x + 3, performing long division or synthetic division will result in a remainder of 0, indicating that it is a factor.
6. For option F. 5x - 3, performing long division or synthetic division will result in a remainder, indicating that it is not a factor.

Therefore, the correct answers are: B. x - 3, C. x² + 6x + 9, and E. x + 3.