Factoring Quadratic Expressions

The video tutorial covers various factoring techniques, starting with an introduction to special factor patterns and monic quadratics. It explains the difference of squares, highlighting the importance of perfect squares and the pattern a^2 - b^2 = (a + b)(a - b). The tutorial then moves to perfect square trinomials, showing how they can be factored into a binomial squared. Finally, it addresses non-monic quadratics, emphasizing the need for guessing and checking to find the correct factors when the leading coefficient is not one.

What is the first step in factoring a monic quadratic equation?

• Use the quadratic formula

• Identify the greatest common factor

• Complete the square

• Find two numbers that multiply to the constant term and add to the middle term

In the context of factoring, what does the term 'monic' refer to?

• The constant term is zero

• The leading coefficient is one

• The middle term is zero

• The quadratic has no real roots

Which of the following is a characteristic of a difference of squares?

• It can be factored as (a + b)(a - b)

• It always results in a positive product

• It requires completing the square

• It involves three terms

What is the result of factoring x^2 - 9?

• (x + 3)(x + 3)

• (x - 3)(x + 3)

• (x - 3)(x - 3)

• (x - 9)(x + 9)

How can you recognize a perfect square trinomial?

• It always has a negative constant term

• It can be factored into two different binomials

• It has three distinct terms

• It has a middle term that is twice the product of the square roots of the first and last terms

Which of the following expressions is a perfect square trinomial?

• x^2 + 4x + 4

• x^2 + 6x + 9

• x^2 - 9

• x^2 - 4x + 4

What is the factored form of 4x^2 - 12x + 9?

• (4x - 3)(x - 3)

• (2x - 3)^2

• (2x - 3)(x - 3)

• (2x + 3)(2x - 3)

What is a key difference when factoring non-monic quadratics compared to monic quadratics?

• The quadratic formula is used

• The leading coefficient is one

• The process involves guessing and checking

• The constant term is always positive

What is the factored form of 2x^2 - 11x - 6?

• (2x + 1)(x - 6)

• (2x - 3)(x + 2)

• (2x - 6)(x + 1)

• (2x + 3)(x - 2)

When factoring non-monic quadratics, why is it important to consider the greatest common factor (GCF)?

• It ensures the equation is in standard form

• It eliminates the need for guessing and checking

• It changes the sign of the constant term

• It simplifies the expression, making it easier to factor