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: $(a) \quad 2x^2 - 3x - 2 = 0$ $(b) \quad x^4 - 5x^2 + 6 = 0$

Would you like detailed solutions for each part of this exercise?