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The image contains two problems involving cubic equations (third-degree equations) to solve and verify. Let's break them down:

### Problem 1:
Given the function \( f(x) = x^3 - 2x^2 - 5x + 6 \), the goal is to solve the equation \( f(x) = 0 \).

#### Steps:
1. **a)** Verify that \( x = 1 \) is a solution of the equation \( f(x) = 0 \).
   
   This means substituting \( x = 1 \) into the equation \( f(x) \) and checking if the result is 0.

2. **b)** Show that the cubic function can be written in the form \( (x - 1)(ax^2 + bx + c) \) by expanding and identifying the coefficients of \( a \), \( b \), and \( c \).

3. **c)** Solve the quadratic equation \( ax^2 + bx + c = 0 \).

4. **d)** Deduce all the solutions of the equation \( f(x) = 0 \), by factoring it completely.

### Problem 2:
Solve the equation \( 2x^3 - 20x^2 - 618x + 1980 = 0 \).

#### Steps:
1. **a)** Verify that \( x = 3 \) is a solution of this equation. Then factor the cubic polynomial by expressing it as \( (x - 3)g(x) \), where \( g(x) \) is a quadratic polynomial.

2. **b)** Find all the solutions of the equation by solving the quadratic polynomial \( g(x) = 0 \).

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### Relative Questions:
1. How do we confirm whether a given value is a solution to a cubic equation?
2. What is the process for factoring a cubic polynomial?
3. How can we determine the coefficients when rewriting a cubic equation as a product of a linear and quadratic term?
4. What methods can we use to solve quadratic equations?
5. How can we use factoring to find all solutions of a cubic equation?

### Tip:
When verifying if a specific value is a solution, always substitute the value into the equation and simplify to check if the result is zero.

Solve the cubic equations: 1) f(x) = x^3 - 2x^2 - 5x + 6 = 0, and 2) 2x^3 - 20x^2 - 618x + 1980 = 0.

Explore how to solve cubic equations such as f(x) = x^3 - 2x^2 - 5x + 6 = 0 and 2x^3 - 20x^2 - 618x + 1980 = 0. Learn key algebraic concepts, including root verification, factoring, and solving quadratic equations. Suitable for high school students in Grades 10-12.

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