Solving Linear Equations and Factoring

This video tutorial covers the process of factoring quadratic equations using the grouping method. It begins with an introduction to the technique, followed by two detailed examples demonstrating how to apply the method. The first example shows how to factor a polynomial already partially factored, while the second example involves factoring a more complex polynomial. The video concludes with a summary of the solutions obtained from each example.

What is the main technique reviewed in this video?

• Factor by grouping

• Completing the square

• Quadratic formula

• Synthetic division

In the first example, what is the common binomial factor identified?

• 2X - 3

• 3X - 1

• X + 1

• X - 1

What is the solution for the equation 2X - 3 = 0?

• X = 0

• X = -1

• X = 3/2

• X = 1

What is the solution for the equation X + 1 = 0?

• X = -1

• X = 3/2

• X = 0

• X = 1

In the second example, what is the greatest common factor on the left side?

• 1

• 3X

• X - 1

• 2X - 3

What is the common binomial factor in the second example?

• X + 1

• X - 1

• 3X - 1

• 2X - 3

What is the solution for the equation X - 1 = 0?

• X = 0

• X = -1

• X = 3/2

• X = 1

What is the solution for the equation 3X - 1 = 0?

• X = 1

• X = 3/2

• X = 1/3

• X = 0

What is the purpose of factoring out a 1 in the examples?

• To simplify the equation

• To solve the equation directly

• To find the greatest common factor

• To create a common binomial factor

What is the final step after factoring in both examples?

• Distribute the factors

• Combine like terms

• Solve the resulting equations

• Add constants to both sides