Final answer:
To find the polynomial that must be added to -5x + 2x - 5 so that the sum is 3x - x - 1, the polynomial that must be added is 2x - 5.
Step-by-step explanation:
To find the polynomial that must be added to -5x + 2x - 5 so that the sum is 3x - x - 1, we need to combine like terms on both sides of the equation. On the left side, -5x + 2x simplifies to -3x. On the right side, 3x - x simplifies to 2x. Therefore, the polynomial that must be added is 2x - 5.