Factoring Polynomials and Properties

This video tutorial explains how to factor a difference of squares by recognizing perfect square terms in a binomial. It provides examples such as X^2 - 25, X^2 - 81, 64X^2 - 49, and X^4 - 16, demonstrating the process of factoring and verifying results. The tutorial also covers factoring with a common factor, emphasizing the importance of identifying perfect squares and differences. The video concludes with a summary of key concepts and examples.

What is the formula for factoring a difference of squares?

• (A - B)(A - B)

• (A + B)(A + B)

• (A + B)(A - B)

• (A + B + C)(A - B - C)

Which of the following is a perfect square?

• X^7

• X^5

• X^3

• X^2

How does the commutative property of multiplication affect factoring?

• It allows changing the order of factors.

• It has no effect on factoring.

• It prevents changing the order of factors.

• It requires factors to be in alphabetical order.

What is the result of factoring X^2 - 81?

• (X + 9)(X - 9)

• (X + 8)(X - 8)

• (X + 10)(X - 10)

• (X + 7)(X - 7)

What is the first step in factoring 64X^2 - 49?

• Subtract the terms.

• Add the terms together.

• Multiply the terms.

• Recognize both terms as perfect squares.

What are the factors of 64X^2 - 49?

• (8X + 7)(8X - 7)

• (8X + 6)(8X - 6)

• (8X + 5)(8X - 5)

• (8X + 4)(8X - 4)

Why can't a sum of squares be factored?

• It is already in simplest form.

• It is considered prime.

• It can be factored using complex numbers.

• It has no real solutions.

What additional step is needed when factoring X^4 - 16?

• Add a constant term.

• Factor further if possible.

• Multiply by a coefficient.

• Divide by a common factor.

What is the greatest common factor in the expression 2X^2 - 18?

• 6

• 3

• 9

• 2

After factoring out the greatest common factor, what is the result of 2X^2 - 18?

• 2(X^2 - 9)

• 2(X^2 - 8)

• 2(X^2 - 7)

• 2(X^2 - 6)