Factoring Differences of Squares

The video tutorial covers the topic of factoring a difference of perfect squares. It begins with an introduction to the concept and the essential question of how to factor special binomials. The tutorial explains the steps to factor a difference of perfect squares, including recognizing perfect squares and using the subtraction sign. It provides examples and practice problems to reinforce the learning. The video also discusses the importance of identifying the greatest common factor (GCF) before factoring and highlights polynomials that cannot be factored, known as prime polynomials.

What is the result of factoring the binomial x^2 - 16?

• (x + 4)(x + 4)

• (x - 4)(x - 4)

• (x + 4)(x - 4)

• (x - 4)(x + 4)

Which of the following is a necessary condition for a binomial to be a difference of squares?

• Both terms must be prime numbers.

• It must have a plus sign between the terms.

• Both terms must be perfect squares.

• It must have a multiplication sign between the terms.

What is the factored form of 4a^2 - 9b^2?

• (4a + 9b)(4a - 9b)

• (4a - 9b)(4a + 9b)

• (2a - 3b)(2a - 3b)

• (2a + 3b)(2a - 3b)

If you cannot take the square root of both terms in a binomial, what should you check for first?

• A common exponent

• A common variable

• A common factor

• A common coefficient

What is the greatest common factor (GCF) of 24x^3 and 6x?

• 6x

• 12x

• 3x

• 24x

What is the factored form of 64x^2 - 16y^2?

• (64x - 16y)(64x + 16y)

• (8x + 4y)(8x - 4y)

• (8x - 4y)(8x - 4y)

• (64x + 16y)(64x - 16y)

What is the factored form of 81x^2 - 100?

• (81x + 100)(81x - 100)

• (9x + 10)(9x - 10)

• (81x + 10)(81x - 10)

• (9x - 10)(9x - 10)

What is the factored form of 9r^2 - 4?

• (9r + 4)(9r - 4)

• (9r + 2)(9r - 2)

• (3r - 2)(3r - 2)

• (3r + 2)(3r - 2)

Which of the following is an example of a prime polynomial?

• 16x^2 - 25

• 9x^2 - 1

• 7x + 19

• x^2 - 4

What should you write if a polynomial cannot be factored?

• None

• Zero

• Prime

• Undefined