Factoring Expressions and Strategies

The video tutorial demonstrates how to factor the expression 100x squared minus 400. It begins by identifying the greatest common factor (GCF) of 100, which simplifies the expression to x squared minus 4. The tutorial then applies the difference of squares method to further factor the expression into (x + 2)(x - 2), while keeping the GCF of 100. The final solution is verified by multiplying the factors back to ensure they match the original expression. The video emphasizes the importance of choosing the right factoring strategy and provides a step-by-step guide to solving the problem.

What is the expression we are trying to factor in this video?

• 100x² + 4

• x² - 4

• 100x² - 400

• 100x² + 400

What is the first step in any factoring problem?

• Multiply the terms

• Identify the greatest common factor

• Check for a difference of squares

• Add the terms

What is the greatest common factor in the expression 100x² - 400?

• 10

• 100

• 20

• 50

After factoring out the GCF, what expression is left inside the parentheses?

• x² + 2

• x² - 2

• x² - 4

• x² + 4

What should you consider when there are two terms inside the parentheses?

• Look for a sum of squares

• Look for a difference of squares

• Look for a difference of cubes

• Look for a sum of cubes

What is the square root of x²?

• 4x

• x²

• 2x

• x

What is the square root of 4?

• 1

• 2

• 3

• 4

What are the factors of x² - 4 using the difference of squares?

• (x + 2)(x - 2)

• (x + 4)(x - 4)

• (x + 3)(x - 3)

• (x + 1)(x - 1)

What is the final factored form of 100x² - 400?

• 100(x + 1)(x - 1)

• 100(x + 2)(x - 2)

• 100(x + 4)(x - 4)

• 100(x + 3)(x - 3)

What is the purpose of multiplying the factors back together?

• To verify the factored solution

• To add the terms

• To find a new expression

• To simplify the expression