Factoring Quadratic Equations and Concepts

The video tutorial focuses on factoring quadratic equations where the leading coefficient 'a' is not equal to one. The instructor begins by explaining the standard form of a quadratic equation and demonstrates how to extract a common factor from all terms. By taking out a negative factor, the equation is simplified, allowing the use of the diamond method to find factors that multiply to a specific product and add to a specific sum. The tutorial concludes with the final factored form of the equation, emphasizing the importance of not forgetting the extracted factor.

What is the standard form of a quadratic equation?

• ax^2 + bx = 0

• ax^2 + bx + c = 0

• ax + b = 0

• ax^2 + c = 0

If a quadratic equation has a coefficient of x^2 as -2, what can be factored out from all terms?

• 2

• -2

• 1

• -1

What is the result of factoring out -2 from -2x^2?

• -x^2

• 2x^2

• x^2

• -x

What is the simplified form of 72 divided by 2?

• 34

• 36

• 38

• 40

In the diamond method, what do you place at the bottom of the diamond?

• c

• a * c

• a + c

• b

What is the product of a and c if a is 1 and c is -36?

• 1

• -36

• 36

• -1

Which two numbers multiply to -36 and add up to -9?

• 12 and -3

• -6 and 6

• 6 and -6

• -12 and 3

What is the factored form of x^2 - 9x - 36?

• (x - 6)(x + 6)

• (x + 6)(x - 6)

• (x + 12)(x - 3)

• (x - 12)(x + 3)

What should you not forget to include in the final factored form after taking out a common factor?

• The original equation

• The common factor

• The variable x

• The constant term

What is the final factored form of the quadratic equation given in the tutorial?

• 2(x + 12)(x - 3)

• -2(x - 12)(x + 3)

• 2(x - 12)(x + 3)

• -2(x + 12)(x - 3)