Question

Can someone solve this step by step I cannot understand this 😭

Answer 1

What hold up

Answer 2

@oliver69

Answer 3

Get over here

Answer 4

To find the degree of the polynomial that produces the given successive results, we analyze the sequence of differences until we find a constant difference. Here are the successive results: 24, 0, -24, 0, 144, 504.

Let's go through the steps to find the differences:

1. First differences:
\[ 0 - 24 = -24 \]
\[ -24 - 0 = -24 \]
\[ 0 - (-24) = 24 \]
\[ 144 - 0 = 144 \]
\[ 504 - 144 = 360 \]
So, the first differences are: -24, -24, 24, 144, 360.

2. Second differences:
\[ -24 - (-24) = 0 \]
\[ 24 - (-24) = 48 \]
\[ 144 - 24 = 120 \]
\[ 360 - 144 = 216 \]
So, the second differences are: 0, 48, 120, 216.

3. Third differences:
\[ 48 - 0 = 48 \]
\[ 120 - 48 = 72 \]
\[ 216 - 120 = 96 \]
So, the third differences are: 48, 72, 96.

4. Fourth differences:
\[ 72 - 48 = 24 \]
\[ 96 - 72 = 24 \]
So, the fourth differences are: 24, 24, which is constant.

Since it took four levels of differences to reach a constant difference, the degree of the polynomial is 4.

Therefore, the correct answer is: 4

I hope this helps you