Factoring Special Cases of Trinomials

This video tutorial covers unit 8, lesson 5 on special factors, focusing on recognizing patterns in perfect square trinomials and the difference of squares. The instructor explains how to identify these patterns and apply them to factor expressions efficiently. Several example problems are solved to demonstrate the application of these concepts, including factoring trinomials and calculating perimeters of squares. The video also introduces shortcuts for factoring, such as the difference of squares formula.

What does the FOIL method help us determine when squaring a binomial?

• The product of two distinct binomials

• The difference of squares

• The sum of the product of the outer and inner terms

• The pattern of a perfect square trinomial

In the expression (x + 5)^2, what does '5' represent in the context of factoring?

• The constant term in a binomial

• The variable term's coefficient

• The square root of the last term

• The coefficient of x

What is the correct factorization of x^2 + 10x + 25?

• (x + 10)(x + 2.5)

• (x + 2.5)(x + 2.5)

• (x - 5)(x - 5)

• (x + 5)(x + 5)

Which expression correctly represents a perfect square trinomial?

• x^2 + xy - y^2

• x^2 - xy + y^2

• x^2 - 2xy + y^2

• x^2 + 2xy + y^2

If a trinomial fits the perfect square pattern, what can be immediately determined?

• Its degree

• Its discriminant

• Its roots

• Its coefficients

How does introducing a negative sign affect the factoring of a trinomial?

• It invalidates the perfect square pattern

• It changes the signs of the factors

• It does not affect the factors

• It requires the use of absolute values

What does the expression (2x + 1)^2 expand to?

• 4x^2 + 4x + 1

• 4x^2 + 2x + 1

• 2x^2 + 2x + 1

• 4x^2 - 4x + 1

What is the perimeter of a square with the area represented by x^2 + 18x + 81?

• x + 9

• 2x + 18

• 4x + 36

• 18x + 81

What is the factored form of x^2 - 25?

• (x - 5)(x + 5)

• (x + 5)(x - 5)

• (x - 25)(x + 25)

• (x + 25)(x - 25)

Which scenario describes the difference of squares pattern?

• Two binomials added and then squared

• A binomial multiplied by its conjugate

• A binomial squared minus another binomial squared

• Two distinct binomials multiplied