Someone help me please

Question

Use finite differences to determine the degree of the polynomial function that fits the 

data.

1	2	3	4	5
1	4	23	70	157

Answer 1

SOLUTION

First-order differences:

Δy₁=4−1=3

Δy₂=23−4=19

Δy₃=70−23=47

Δy₄=157−70=877​

Second-order differences:

Δ²y₁=19−3=16

Δ²y₂=47−19=28

Δ²y₃=87−47=40

Third-order differences:

Δ³y₁=28−16=12

Δ³y₂=40−28=12

Now, let's summarize the findings:

1. First-order differences: Not constant.
2. Second-order differences: Not constant.
3. Third-order differences: Constant.

The degree of the polynomial will be one less than the smallest number of differences needed to find a constant sequence.

Hence, the degree of the polynomial function to represent the data accurately is 2.