Factoring Quadratic Expressions and GCF

The video tutorial explains how to solve quadratic equations by factoring. It emphasizes the importance of factoring out the greatest common factor (GCF) as the first step. Two examples are provided: the first involves factoring a quadratic equation with a GCF, and the second involves factoring a trinomial with a non-unit leading coefficient. The tutorial concludes by reiterating the importance of identifying and factoring out the GCF to simplify the process.

What is the first step in solving a quadratic equation by factoring?

• Set the equation to zero

• Find the roots of the equation

• Multiply all terms by the leading coefficient

• Factor out the greatest common factor

In the first example, what is the greatest common factor of 5x^2 - 45?

• 45

• 5

• 9

• x

What type of expression is x^2 - 9 in the first example?

• Linear binomial

• Perfect square trinomial

• Difference of squares

• Sum of squares

What are the solutions for the equation 5(x^2 - 9) = 0?

• x = 9 or x = -9

• x = 5 or x = -5

• x = 0

• x = 3 or x = -3

In the second example, what is the greatest common factor of 3x^2 - 6x - 45?

• 15

• x

• 6

• 3

What is the leading coefficient of the trinomial after factoring out the greatest common factor in the second example?

• 3

• 2

• 1

• 0

Which pair of numbers are the factors of -15 that add up to -2 in the second example?

• -3 and 5

• -1 and 15

• -5 and 3

• -2 and 7

What are the solutions for the equation 3(x^2 - 2x - 15) = 0?

• x = 15 or x = -15

• x = 0

• x = 5 or x = -3

• x = 3 or x = -5

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

• It simplifies the equation

• It changes the equation

• It eliminates the variable

• It increases the degree of the equation

What happens if you don't factor out the greatest common factor?

• The equation becomes more difficult

• The equation remains unchanged

• The equation becomes easier

• The equation has no solution