The successive differences for a sequence are shown. What is the standard form polynomial that represents the sequence? (1 point) Responses 2x2+9x+7 2 x squared plus 9 x plus 7 4x2−x +12 4x2−x +12 3x2+8x−5 3 x squared plus 8 x minus 5 2x2+4x −3 2x2+4x −3 Skip to navigation

To find the standard form polynomial that represents the given sequence based on the successive differences, we need to analyze the differences that were provided and possibly the pattern they follow.

Since the sequences or differences are not explicitly given in your question, I'll explain the general method to determine the polynomial from successive differences, and you can apply it.

1. **Calculate the successive differences**: If you have the original sequence values, list them and calculate the first differences (the difference between consecutive terms), then the second differences, and so on.

2. **Identify the degree of the polynomial**:
- If the first differences are constant, the polynomial is of degree 1 (linear).
- If the second differences are constant, the polynomial is of degree 2 (quadratic).
- If the third differences are constant, the polynomial is of degree 3 (cubic), and so forth.

3. **Form the polynomial**: The form of the polynomial will be derived from the constant differences noted:
- For a quadratic polynomial, it looks like \( ax^2 + bx + c \).

4. **Choose the appropriate polynomial**: From the responses provided:
- **2x² + 9x + 7**
- **4x² - x + 12**
- **3x² + 8x - 5**
- **2x² + 4x - 3**

You would match the differences and your calculated constant differences to one of the provided polynomial options.

If you have the original sequence or the differences that led to these choices, I can assist more specifically. If not, review the polynomial to see if the pattern matches the ones you've listed.