Question

Which polynomial sequence shows that the terms of the 2nd differences are constant?

a) 2x² - 4x + 3
b) 3x³ - 6x² + 3x - 5
c) 4x⁴ - 8x³ + 4x² + 3x - 1
d) 5x⁵ - 10x⁴ + 5x³ - 2x + 3

Answer 1

The polynomial sequence that shows constant terms of the 2nd differences is option a) 2x² - 4x + 3.

Step-by-step explanation:

The polynomial sequence that shows constant terms of the 2nd differences is option a) 2x² - 4x + 3.

To determine if the terms of the 2nd differences are constant, we need to find the differences between consecutive terms and then find the differences between those differences.

Let's calculate the 2nd differences for option a) 2x² - 4x + 3:

1. First differences: 4x - 4
2. 2nd differences: 4