https://r2.erweima.ai/mathbot/image/1726595081217byo6wxg5.jpg

The expression in the image is as follows:

\[
-3x^3 - 2x^2 + 5x^3 + 4x^4 - 2x^2 + x - 7x + 5
\]

Let's simplify this step by step.

### Step 1: Combine like terms
Group the terms with the same powers of \(x\).

- \(x^4\) terms: \(4x^4\)
- \(x^3\) terms: \(-3x^3 + 5x^3\)
- \(x^2\) terms: \(-2x^2 - 2x^2\)
- \(x\) terms: \(x - 7x\)
- Constant term: \(5\)

### Step 2: Perform the arithmetic

- For \(x^3\): \(-3x^3 + 5x^3 = 2x^3\)
- For \(x^2\): \(-2x^2 - 2x^2 = -4x^2\)
- For \(x\): \(x - 7x = -6x\)

### Final simplified expression:
\[
4x^4 + 2x^3 - 4x^2 - 6x + 5
\]

This is the fully simplified polynomial.

Would you like further details or have any questions about this process?

Here are some related questions you might explore:
1. How do you solve a polynomial equation like this for its roots?
2. What are the different methods to factor polynomials?
3. How can you find the derivative of this polynomial?
4. What role does the degree of a polynomial play in graphing it?
5. How do you perform synthetic division on this polynomial?

**Tip:** Always organize your polynomial terms by the degree (highest power first) when simplifying or solving them.

Simplify the polynomial expression -3x^3 - 2x^2 + 5x^3 + 4x^4 - 2x^2 + x - 7x + 5.

This problem involves simplifying a polynomial expression by combining like terms. Learn how to identify terms with the same powers of x and simplify step by step.

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