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Rewrite [tex] \frac{2x^6 - 9x^5 + 4x^2 - 5}{x^3 - 5} [/tex] in the form [tex] q(x) + \frac{r(x)}{b(x)} [/tex]. What is [tex] q(x) [/tex]?

A. [tex] 2x^9 - 9x^8 - 10x^6 + 49x^5 - 5x^3 - 20x^2 + 25 [/tex]

B. [tex] 2x^6 - 9x^5 + 4x^2 - 5 [/tex]

C. [tex] 2x^3 - 9x^2 + 4x - 5 [/tex]

D. [tex] 2x^3 - 9x^2 + 10 [/tex]

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GinnyAnswer
To solve the problem of rewriting [tex]\(\frac{2x^6 - 9x^5 + 4x^2 - 5}{x^3 - 5}\)[/tex] in the form [tex]\(q(x) + \frac{r(x)}{b(x)}\)[/tex], we need to perform polynomial division where:

- The dividend is [tex]\(2x^6 - 9x^5 + 4x^2 - 5\)[/tex]
- The divisor is [tex]\(x^3 - 5\)[/tex]

In the polynomial division, the quotient [tex]\(q(x)\)[/tex] is the result of the division, and [tex]\(r(x)\)[/tex] is the remainder.

Given the result from the polynomial division, the quotient [tex]\(q(x)\)[/tex] is:

[tex]\[2x^3 - 9x^2 + 10\][/tex]

Thus, the correct answer is:
[tex]\[q(x) = \boxed{2x^3 - 9x^2 + 10}\][/tex]

So, the answer is:

D. [tex]\(2 x^3 - 9 x^2 + 10\)[/tex]
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