Factoring and Properties of Polynomials

This video tutorial teaches how to recognize and factor perfect square polynomials. It begins with an example of factoring a simple polynomial and explains the characteristics that make a polynomial a perfect square. The tutorial then generalizes the concept using variables and demonstrates how to apply this understanding to different polynomial forms. The video emphasizes the importance of recognizing patterns and using the distributive property to verify factored forms.

What is the product of the two numbers needed to factor the polynomial x^2 + 6x + 9?

• 9

• 15

• 6

• 12

Which two numbers add up to 6 and multiply to 9 in the polynomial x^2 + 6x + 9?

• 1 and 9

• 2 and 4

• 3 and 3

• 5 and 1

In the polynomial a^2 + 14a + 49, what is the perfect square constant term?

• 7

• 21

• 49

• 14

What is the coefficient of the first-degree term in the polynomial a^2 + 14a + 49?

• 28

• 7

• 14

• 21

What is the result of squaring the expression (A + B)?

• A^2 + 2A + B^2

• A^2 + B^2

• A^2 + AB + B^2

• A^2 + 2AB + B^2

Which property is used twice to verify the factorization of a perfect square polynomial?

• Associative Property

• Identity Property

• Commutative Property

• Distributive Property

What is the general form of a perfect square trinomial?

• A^2 + 2AB + B^2

• A^2 + B^2

• A^2 + 2A + B^2

• A^2 + AB + B^2

In the expression 25 + 10x + x^2, what is the perfect square constant term?

• 5

• 25

• 50

• 10

How can the polynomial 25 + 10x + x^2 be rewritten to recognize it as a perfect square?

• 25 + x^2 + 10x

• x^2 + 10x + 25

• x^2 + 25 + 10x

• 10x + x^2 + 25

What is the coefficient of the first-degree term in the polynomial 25 + 10x + x^2?

• 20

• 15

• 10

• 5