Factoring Polynomials and Expressions

This video tutorial provides a comprehensive guide to factoring various polynomial expressions, including binomials, trinomials, and higher-degree polynomials. It covers specific formulas for the difference and sum of squares and cubes, as well as perfect square trinomials. The tutorial also touches on the binomial theorem and offers additional resources for further learning.

What is the factored form of a difference of squares, a^2 - b^2?

• (a + b)(a - b)

• (a - b)(a - b)

• (a + b)(a + b)

• (a^2 - b^2)

How do you factor the sum of two cubes, a^3 + b^3?

• (a - b)(a^2 - ab + b^2)

• (a - b)(a^2 + ab + b^2)

• (a + b)(a^2 - ab + b^2)

• (a + b)(a^2 + ab + b^2)

What is the factored form of a difference of cubes, a^3 - b^3?

• (a - b)(a^2 + ab + b^2)

• (a + b)(a^2 - ab + b^2)

• (a - b)(a^2 - ab + b^2)

• (a + b)(a^2 + ab + b^2)

How does the sign pattern differ when factoring a^5 - b^5 compared to a^5 + b^5?

• The signs are all negative in a^5 + b^5

• The signs are all positive in a^5 - b^5

• The signs alternate in a^5 - b^5

• The signs alternate in a^5 + b^5

What is the general pattern for the signs in the expression a^5 + b^5?

• Signs are all positive except the last term

• All terms are negative

• All terms are positive

• Signs alternate between positive and negative

What is the factored form of a perfect square trinomial, a^2 + 2ab + b^2?

• (a + b)^2

• (a - b)^2

• (a + b)(a - b)

• (a^2 + b^2)

How do you factor a trinomial of the form a^2 - 2ab + b^2?

• (a + b)(a - b)

• (a + b)^2

• (a - b)^2

• (a^2 - b^2)

What is the factored form of a polynomial a^3 + 3a^2b + 3ab^2 + b^3?

• (a + b)^3

• (a - b)(a^2 + ab + b^2)

• (a - b)^3

• (a + b)(a^2 - ab + b^2)

Which expression represents the binomial theorem for a^3 - 3a^2b + 3ab^2 - b^3?

• (a + b)(a^2 - ab + b^2)

• (a - b)(a^2 + ab + b^2)

• (a + b)^3

• (a - b)^3

Where can you find additional factoring formulas not covered in the video?

• In the video itself

• In the description section below the video

• In the comments section

• In the video title