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------------------------------------------------ Divide and simplify.

[tex]
\frac{-20x^{10} + 8x^9 + 4x^8}{4x^8} = \square
[/tex]

Sure! Let's divide and simplify the expression step-by-step:

We have the expression:

[tex]\[
\frac{-20x^{10} + 8x^9 + 4x^8}{4x^8}
\][/tex]

### Step 1: Break Down the Expression

To simplify, divide each term in the numerator by the denominator separately:

1. The first term: [tex]\(\frac{-20x^{10}}{4x^8}\)[/tex]
2. The second term: [tex]\(\frac{8x^9}{4x^8}\)[/tex]
3. The third term: [tex]\(\frac{4x^8}{4x^8}\)[/tex]

### Step 2: Simplify Each Term

1. Simplify [tex]\(\frac{-20x^{10}}{4x^8}\)[/tex]:

- Coefficient: [tex]\(\frac{-20}{4} = -5\)[/tex]
- Variables: [tex]\(\frac{x^{10}}{x^8} = x^{10-8} = x^2\)[/tex]

Result: [tex]\(-5x^2\)[/tex]

2. Simplify [tex]\(\frac{8x^9}{4x^8}\)[/tex]:

- Coefficient: [tex]\(\frac{8}{4} = 2\)[/tex]
- Variables: [tex]\(\frac{x^9}{x^8} = x^{9-8} = x\)[/tex]

Result: [tex]\(2x\)[/tex]

3. Simplify [tex]\(\frac{4x^8}{4x^8}\)[/tex]:

- Coefficient: [tex]\(\frac{4}{4} = 1\)[/tex]
- Variables: [tex]\(\frac{x^8}{x^8} = x^{8-8} = x^0 = 1\)[/tex]

Result: [tex]\(1\)[/tex]

### Step 3: Combine the Results

Combine the simplified terms:

[tex]\[
-5x^2 + 2x + 1
\][/tex]

So, the simplified expression is:

[tex]\[
-5x^2 + 2x + 1
\][/tex]

This is the final simplified form.