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The image shows an exercise involving algebraic expressions, specifically tasks related to factoring and simplifying quadratic forms. Here's the breakdown of the problems presented:

### Exercise:
1. **Factor completely**:
   \[
   (a) \quad 3x^2 - 9x + 6 = 0
   \]
   \[
   (b) \quad x^3 - 8x^2 + 17x - 10 = 0
   \]

2. **Factor and simplify**:
   \[
   \frac{(3x + 1) - \frac{x(2x + 1)}{2}}{(x + 1)^2} = \frac{3}{x + 1}
   \]

3. **Apply the linear factorization theorem**:
   \[
   2x^3 - 5x^2 + 3x - 6 = 0
   \]

4. **Simplify and solve**:
   \[
   (a) \quad 2x^2 - 3x - 2 = 0
   \]
   \[
   (b) \quad x^4 - 5x^2 + 6 = 0
   \]

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Solve the algebraic expressions and equations given in the exercise, including factoring, simplifying, and applying the linear factorization theorem.

This exercise focuses on solving algebraic expressions by factoring quadratic and cubic equations, simplifying complex fractions, and applying the linear factorization theorem. Suitable for high school students in Grades 10-12.

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