Factoring Polynomials: A Comprehensive Challenge

This video tutorial covers various factoring techniques, including identifying the greatest common factor, factoring trinomials, and using the difference of squares and sum/difference of cubes methods. The instructor provides step-by-step examples and encourages viewers to practice with a free worksheet. The video aims to enhance understanding and skills in factoring polynomials.

What is the first step in factoring a polynomial?

• Identify the leading coefficient

• Find the greatest common factor

• Split the middle term

• Draw a box method diagram

What does the acronym SOAP stand for in the context of factoring?

• Sum, Opposite, Addition, Power

• Square, Open, Apply, Process

• Subtract, Obtain, Add, Positive

• Same, Opposite, Always Positive

When factoring a difference of squares, what pattern do you use?

• a^2 + b^2 = (a - b)(a + b)

• a^2 - b^2 = (a + b)(a - b)

• a^2 + b^2 = (a + b)^2

• a^2 - b^2 = (a - b)^2

In the AC method of factoring, what does 'AC' stand for?

• Addition and Calculation

• Algebraic Coefficients

• Advanced Calculus

• A times C

What is a perfect square trinomial?

• A trinomial that cannot be factored

• A trinomial where the first and last terms are perfect squares

• A trinomial with a leading coefficient of 1

• A trinomial that factors into a binomial squared

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

• a^2 - b^2 = (a + b)^2

• a^2 - b^2 = a^2 + 2ab + b^2

• a^2 - b^2 = (a + b)(a - b)

• a^2 - b^2 = (a - b)^2

What is the factored form of x^3 - 8?

• x^3 - 8 = (x - 2)^3

• x^3 - 8 = (x + 2)(x^2 - 2x + 4)

• x^3 - 8 = (x - 2)(x^2 + 2x + 4)

• x^3 - 8 = (x + 2)^3

Which of the following is a method for factoring a polynomial?

• Cross multiplication

• Factoring by grouping

• Long division

• Synthetic division

How do you factor a trinomial with a leading coefficient not equal to one?

• Use the sum of cubes formula

• Apply the difference of squares formula

• Factor out the greatest common factor

• Use the AC method

What is the first step in factoring a polynomial?

• Factor out the greatest common factor

• Identify the type of polynomial

• Apply the quadratic formula

• Split the middle term