Factoring and Polynomial Concepts

This video tutorial covers advanced factoring techniques in Algebra 2, including the sum and difference of cubes, factoring by grouping, and recognizing quadratic form in higher-degree polynomials. The instructor provides examples and practice problems to reinforce these concepts, helping students understand how to factor and solve polynomial equations effectively.

Which of the following is NOT a type of factoring discussed in this lesson?

• Quadratic form

• Sum and difference of cubes

• Factoring by grouping

• Factoring by substitution

What is the acronym used to remember the formula for the sum and difference of cubes?

• PEMDAS

• FOIL

• SOAP

• BODMAS

In the sum and difference of cubes formula, what does the 'O' in SOAP stand for?

• Order

• Opposite

• Operation

• Original

When factoring by grouping, how many terms should you typically start with?

• Two

• Five

• Three

• Four

What is the first step in factoring by grouping?

• Divide the terms

• Multiply the terms

• Factor out the greatest common factor

• Combine like terms

In the quadratic form of factoring, what is the relationship between the middle and leading exponents?

• The middle exponent is double the leading exponent

• The middle exponent is half of the leading exponent

• The middle exponent is equal to the leading exponent

• The middle exponent is one less than the leading exponent

Which of the following is an example of a polynomial in quadratic form?

• x^4 + 5x^2 + 6

• x^2 + 4x + 4

• x^5 + 2x^3 + 1

• x^3 + 3x^2 + 3x + 1

What is the first step in solving a polynomial equation after factoring?

• Add all terms

• Divide by the leading coefficient

• Set each factor equal to zero

• Multiply all factors

Which of the following represents a difference of two squares?

• x^4 + 16

• x^3 - 27

• x^2 - 9

• x^2 + 4x + 4

What is the result of factoring the expression 4x^3 - 36x?

• 4(x^3 - 9x)

• 4x(x^2 - 9)

• x(4x^2 - 36)

• 4x(x - 3)(x + 3)