Factoring Polynomials and Perfect Squares

The video tutorial covers factoring polynomials, focusing on special cases like the difference of two squares and perfect square trinomials. It explains how to identify these cases and provides examples to illustrate the concepts. The tutorial also outlines the steps to factor these polynomials, including checking for subtraction operations and perfect squares, and applying specific patterns to find the factors.

What is the general form of a difference of two squares?

• a^2 + 2ab + b^2

• a^2 + b^2

• a^2 - b^2

• a^2 - 2ab + b^2

Which operation must be present for a polynomial to be a difference of two squares?

• Subtraction

• Addition

• Multiplication

• Division

In the expression 4x^2 - 81, what is the square root of the first term?

• 4x

• 2x

• 16x

• 8x

What are the factors of 4x^2 - 81?

• (4x + 9)(4x - 9)

• (2x + 9)(2x - 9)

• (4x + 81)(4x - 81)

• (2x + 81)(2x - 81)

For the polynomial 16p^4 - 25, what is the square root of 16p^4?

• 4p^2

• 2p^2

• 8p^2

• 16p^2

What are the factors of 16p^4 - 25?

• (8p^2 + 25)(8p^2 - 25)

• (4p^2 + 25)(4p^2 - 25)

• (8p^2 + 5)(8p^2 - 5)

• (4p^2 + 5)(4p^2 - 5)

In the expression 100a^2 - 36b^6, what is the square root of the second term?

• 12b^3

• 18b^3

• 6b^3

• 36b^3

What are the factors of 100a^2 - 36b^6?

• (20a + 36b^3)(20a - 36b^3)

• (10a + 36b^3)(10a - 36b^3)

• (20a + 6b^3)(20a - 6b^3)

• (10a + 6b^3)(10a - 6b^3)

Why is 64x^2 - 13y not a difference of two squares?

• Both terms are perfect squares

• The operation is addition

• 64x^2 is not a perfect square

• 13y is not a perfect square

What is the general form of a perfect square trinomial?

• a^2 - b^2

• a^2 - 2ab + b^2

• a^2 + b^2

• a^2 + 2ab + b^2