https://file.aiquickdraw.com/mathbot/file/1727422597695fwf168jt.jpg

I see you've uploaded an image of some mathematical work. Let me examine the content.

The image contains a sequence of algebraic manipulations, solving a polynomial equation. Here's a breakdown:

- The work seems to involve simplifying and solving a cubic equation for \( x \). It looks like a cubic polynomial, possibly of the form:

  \[
  5x^3 - 4x^2 + 3x - 7
  \]
  
  is being simplified, then further terms are reduced or canceled out, likely leading to a factored form.

- Toward the right side, there is a fraction \( \frac{b}{2} = \frac{24}{5} \), which seems to be part of solving the equation using substitution or factoring.

- Then, \( x = \frac{b}{a} \) is derived, possibly after dividing or simplifying terms in the equation.

Could you confirm what specific part you would like assistance with (e.g., factoring, solving for roots, etc.)? Or if you'd like, I can try to reconstruct the full solution step-by-step.

Would you like a more detailed explanation of the process? 

Here are some related questions to further your understanding:
1. What methods do you use to factor cubic equations?
2. How do you identify rational roots in a polynomial equation?
3. What role does synthetic division play in solving cubic equations?
4. How does the quadratic formula extend to higher-degree polynomials?
5. What does the discriminant tell you about the number of real solutions in a polynomial?

**Tip:** When dealing with polynomials, always check for possible factoring or simplifications to reduce the degree of the equation before solving!

Solving a cubic polynomial equation by factoring and simplifying.

Learn how to solve a cubic polynomial equation step-by-step by factoring and simplifying. This problem covers important algebraic concepts such as polynomial equations, factoring, and solving cubic equations. Suitable for students in Grades 10-12.

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