Factoring and Perfect Squares Concepts

This lesson covers perfect squares and factoring, focusing on identifying and factoring perfect square trinomials. It explains the importance of these concepts in solving real-world problems, such as finance and construction. The video introduces binomials, perfect square trinomials, and various factoring techniques, providing examples and applications. Advanced methods for factoring polynomials are also discussed, with a focus on using patterns and the power of X method.

What is a perfect square number?

• A number that is a prime number

• A number that is the square of an integer

• A number that is a cube of an integer

• A number that can be divided by 2

Which of the following is a perfect square?

• 20

• 8

• 15

• 16

What is the formula for squaring a binomial (a + b)?

• a^2 + ab + b^2

• a^2 + b^2

• a^2 + 2ab + b^2

• a^2 - 2ab + b^2

In the expression (a - b)^2, what is the sign of the middle term?

• Positive

• Negative

• Zero

• It depends on the values of a and b

What is a perfect square trinomial?

• A trinomial that can be factored into two identical binomials

• A trinomial with three different terms

• A trinomial that cannot be factored

• A trinomial with only positive terms

Which of the following is a perfect square trinomial?

• x^2 + 6x + 9

• x^2 - 4x + 4

• x^2 + 5x + 6

• x^2 + 4x + 4

What is the first step in factoring a polynomial?

• Check for a greatest common factor (GCF)

• Check for a difference of squares

• Check for binomial factors

• Check for a perfect square trinomial

When should you use the difference of squares method?

• When the polynomial has three terms

• When the polynomial has four terms

• When the polynomial has two terms

• When the polynomial is a perfect square trinomial

What is the result of factoring 9x^2 - 3x - 20 using the power of X method?

• (3x + 5)(3x - 4)

• (3x - 5)(3x + 4)

• (3x - 4)(3x + 5)

• (3x + 4)(3x - 5)

Which method is used when the coefficient of the quadratic term is greater than one?

• GCF

• Difference of squares

• Perfect square trinomial

• Grouping