Quadratic Equations and Factoring

This video tutorial covers the process of factoring and solving quadratic equations of the form X^2 + BX + C = 0, where the leading coefficient is 1. The instructor demonstrates two examples: X^2 + 4X - 21 = 0 and X^2 - 6X - 27 = 0. For each example, the video explains how to identify the factors of the constant term that add up to the linear coefficient, leading to the binomial factors. The solutions are then found using the zero product property. The video concludes with a promise of more examples in the next session.

What is the standard form of a quadratic equation?

• ax^2 + bx + c = 0

• ax + b = 0

• ax^2 + bx = 0

• ax^3 + bx^2 + cx + d = 0

In the equation x^2 + 4x - 21 = 0, what are the factors of -21 that add up to 4?

• -7 and 3

• -21 and 1

• -1 and 21

• -3 and 7

What is the factored form of the equation x^2 + 4x - 21 = 0?

• (x - 1)(x + 21)

• (x + 3)(x - 7)

• (x + 1)(x - 21)

• (x - 3)(x + 7)

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

• Divide by the leading coefficient

• Add 5 to both sides

• Multiply all terms by 2

• Set the equation to zero

What are the solutions to the equation (x - 3)(x + 7) = 0?

• x = 3 and x = -7

• x = -3 and x = 7

• x = 3 and x = 7

• x = -3 and x = -7

Which property is used to solve the equation once it is in factored form?

• Zero Product Property

• Distributive Property

• Associative Property

• Commutative Property

What are the factors of -27 that add up to -6 in the equation x^2 - 6x - 27 = 0?

• -27 and 1

• -1 and 27

• -3 and 9

• -9 and 3

What is the factored form of the equation x^2 - 6x - 27 = 0?

• (x - 3)(x + 9)

• (x + 9)(x - 3)

• (x - 9)(x + 3)

• (x + 3)(x - 9)

In the context of quadratic equations, what does it mean for a trinomial to factor into binomials?

• It can be expressed as a product of two binomials

• It can be expressed as a quotient of two binomials

• It can be expressed as a difference of two binomials

• It can be expressed as a sum of two binomials

What are the solutions to the equation (x - 9)(x + 3) = 0?

• x = 9 and x = -3

• x = -9 and x = 3

• x = -9 and x = -3

• x = 9 and x = 3