Factoring and GCF in Algebra

The video tutorial explains how to solve equations by factoring, focusing on identifying and factoring out the greatest common factor (GCF). It demonstrates the process using two examples: 12x^2 + 18x = 0 and 4x^2 - 20x = 0. The tutorial emphasizes the use of prime factorization to find the GCF and applies the zero product property to solve the equations. The video aims to help students understand the factoring process and solve quadratic equations effectively.

What is the first step in solving equations by factoring?

• Completing the square

• Using the quadratic formula

• Identifying the greatest common factor

• Expanding the equation

What is the greatest common factor of 12x^2 and 18x?

• 18x

• 6x

• 12x

• 3x

Why is it helpful to write terms in prime factor form?

• To avoid using the zero product property

• To easily identify common factors

• To simplify the equation

• To make the equation longer

After factoring out the GCF from 12x^2 + 18x, what expression is left?

• 2x + 6

• 6x + 3

• 2x + 3

• 3x + 6

What are the solutions to the equation 12x^2 + 18x = 0?

• x = 0 or x = 3/2

• x = 0 or x = -2/3

• x = 0 or x = -3/2

• x = 0 or x = 2/3

Which property is used to solve the equation after factoring?

• Commutative Property

• Zero Product Property

• Associative Property

• Distributive Property

What is the first step in solving the equation 4x^2 - 20x = 0?

• Divide both sides by 4

• Subtract 20x from both sides

• Add 20x to both sides

• Multiply both sides by 4

What is the greatest common factor of 4x^2 and 20x?

• 2x

• 4x

• 5x

• 10x

After factoring out the GCF from 4x^2 - 20x, what expression is left?

• 4x - 5

• x - 5

• x + 5

• 4x + 5

What are the solutions to the equation 4x^2 - 20x = 0?

• x = 0 or x = -4

• x = 0 or x = 4

• x = 0 or x = -5

• x = 0 or x = 5