Factoring and Solving Equations

The video tutorial explains how to solve equations by factoring, focusing on identifying and factoring out the greatest common factor. Two examples are provided: solving X^2 + 4X = 0 and 14X^2 - 35X = 0. The zero product property is used to find solutions, emphasizing the importance of factoring out the greatest common factor as the first step. The tutorial concludes with a reminder of this key point.

What is the first step in solving an equation by factoring?

• Using the zero product property

• Factoring out the greatest common factor

• Solving for x

• Adding terms on both sides

In the equation x^2 + 4x = 0, what is the greatest common factor?

• 4

• 0

• x

• x^2

After factoring x^2 + 4x = 0, what are the possible solutions for x?

• x = 4 or x = -4

• x = 0 or x = -4

• x = 0 or x = 2

• x = 0 or x = 4

What is the greatest common factor in the equation 14x^2 - 35x?

• 35

• 14

• x

• 7x

How can 14x^2 be expressed in terms of its factors?

• 14 x x

• 7 x 2 x x

• 2 x 7 x x x

• 2 x 7 x x

What is the factored form of 14x^2 - 35x?

• 7(2x - 5)

• 7x(2x - 5)

• x(14x - 35)

• 14x(x - 5)

What are the solutions for x in the equation 7x(2x - 5) = 0?

• x = 7 or x = 5/2

• x = 0 or x = 5/2

• x = 0 or x = 5

• x = 7 or x = 0

What operation is performed after factoring to solve the equation 7x = 0?

• Divide both sides by 7

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 7

Why is it important to factor out the greatest common factor first?

• It eliminates the need for further steps

• It simplifies the equation

• It makes the equation longer

• It changes the equation