https://file.aiquickdraw.com/mathbot/file/1726935964405yzkkq9m6.jpg

The expression in the image is:

\[
\frac{2x^3 - 3x^2 - 23x + 12}{x - 0.5}
\]

This is a division of a cubic polynomial by a linear binomial. We can solve this using polynomial long division or synthetic division. I will proceed using synthetic division since the divisor \(x - 0.5\) suggests that \(x = 0.5\) is a root.

Let me perform the synthetic division to simplify this expression.The result of the synthetic division of \( \frac{2x^3 - 3x^2 - 23x + 12}{x - 0.5} \) is:

\[
2x^2 - 2x - 24
\]

with a remainder of 0. This means the division is exact, and the expression simplifies to:

\[
2x^2 - 2x - 24
\]

Would you like to explore more details, or have any questions?

Here are 5 related questions to expand on the topic:

1. How would you factor the quadratic expression \(2x^2 - 2x - 24\)?
2. How is synthetic division different from polynomial long division?
3. What would happen if the remainder were non-zero in this division?
4. How can you verify the result of synthetic division using multiplication?
5. What are the roots of the simplified quadratic equation \(2x^2 - 2x - 24 = 0\)?

**Tip:** When performing polynomial division, always check if the divisor is a factor of the polynomial to ensure the remainder is zero.

Simplify the expression (2x^3 - 3x^2 - 23x + 12) ÷ (x - 0.5).

This guide walks you through the process of simplifying the cubic polynomial (2x^3 - 3x^2 - 23x + 12) divided by (x - 0.5) using synthetic division. Explore polynomial division concepts and understand how to simplify and analyze the result.

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