Answer :

To solve the given division problem [tex]\(\frac{8x^{10} - 8x^9 + 4x^8}{4x^8}\)[/tex], we'll divide each term in the numerator by the denominator [tex]\(4x^8\)[/tex] separately.

Here's a step-by-step breakdown:

1. Divide each term:

- First term: [tex]\(8x^{10}\)[/tex] divided by [tex]\(4x^8\)[/tex]

[tex]\[
\frac{8x^{10}}{4x^8} = \frac{8}{4} \times x^{10-8} = 2x^2
\][/tex]

- Second term: [tex]\(-8x^9\)[/tex] divided by [tex]\(4x^8\)[/tex]

[tex]\[
\frac{-8x^9}{4x^8} = \frac{-8}{4} \times x^{9-8} = -2x
\][/tex]

- Third term: [tex]\(4x^8\)[/tex] divided by [tex]\(4x^8\)[/tex]

[tex]\[
\frac{4x^8}{4x^8} = \frac{4}{4} \times x^{8-8} = 1
\][/tex]

2. Combine the simplified terms:

- Combine the results from each term:

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

So, the simplified result of [tex]\(\frac{8x^{10} - 8x^9 + 4x^8}{4x^8}\)[/tex] is [tex]\(2x^2 - 2x + 1\)[/tex].

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