Use the image to answer the question.

Question

A diagram shows four rows with numbers and blanks. Horizontal lines are shown between each number or blank in a row, and vertical lines extend from the horizontal lines to the numbers or blanks in the row below, indicating a relationship.

The successive differences of a sequence are shown in this image. What is the degree of its associated polynomial expression?

Answer 1

To determine the degree of the polynomial expression associated with the sequence of numbers and blanks shown in the image, we need to analyze the successive differences.

1. Understanding Successive Differences: When we calculate successive differences of a sequence, we list the differences between consecutive numbers. If we repeat this process (calculating differences of differences), we can continue until we reach a constant difference.

2. Identifying the Degree: The number of times we need to take differences before reaching a constant value represents the degree of the polynomial. Specifically:

   • If it takes one difference to reach a constant, the sequence can be described by a polynomial of degree 1 (linear).
   • If it takes two differences, the polynomial is of degree 2 (quadratic).
   • If it takes three differences, the polynomial is of degree 3 (cubic), and so on.

3. Applying to the Given Sequence: Without the specific numbers from the image, I can't perform the calculations. However, if you count how many times you can compute the differences until a constant is reached, that count gives you the degree of the polynomial expression.

Therefore, please perform the successive differences based on the image you have, and the final count will reveal the degree of the polynomial. If you find it takes \( n \) iterations to reach a constant difference, the associated polynomial will be of degree \( n \).