Factoring Polynomials: Key Concepts and Examples

This video tutorial covers the process of factoring polynomials by grouping, providing examples and guidelines for factoring completely. It demonstrates solving equations using factoring and applies these techniques to a real-life problem involving a terrarium. The tutorial emphasizes the importance of recognizing factorable and unfactorable polynomials and provides step-by-step instructions for each example.

What is the first step in factoring polynomials by grouping?

• Apply the zero product property

• Identify and group terms into pairs

• Extract the highest common factor

• Rewrite the polynomial in standard form

In the example of factoring x^3 + 3x^2 + 2x + 6, what is factored out from the first group?

• 2x

• x^3

• 3x

• x^2

Which of the following is a method to check if a polynomial is factorable?

• All of the above

• Checking for integer solutions

• Finding the GCF of all terms

• Using the distributive property

Which of the following is NOT a step in factoring polynomials completely?

• Applying the quadratic formula

• Factoring out the GCF

• Using the zero product property

• Identifying a difference of squares

What property is used to solve equations by setting the equation to zero and factoring?

• Commutative property

• Distributive property

• Associative property

• Zero product property

What is the correct factored form of 2x^3 + 8x^2 - 10x?

• 2x(x^2 + 4x - 5)

• 2x(x^2 - 4x + 5)

• 2x(x - 5)(x + 1)

• 2x(x + 5)(x - 1)

How is the polynomial x^4 - 28x^2 factored?

• x^2(x^2 - 28)

• x^2(x + 2)(x - 2)

• 7x^2(x + 2)(x - 2)

• 7x^2(x^2 - 4)

In solving the equation 2x^3 + 8x^2 = 10x, what is the first step after rewriting the equation?

• Apply the quadratic formula

• Factor out the GCF from all terms

• Set the equation to zero

• Divide all terms by 2

What is the volume formula for a rectangular prism?

• Length + Width + Height

• Length / Width / Height

• None of the above

• Length x Width x Height

What dimensions are found for the terrarium in the complex problem-solving section?

• Length 24 inches, Width 12 inches, Height 16 inches

• Length 16 inches, Width 12 inches, Height 24 inches

• Length 32 inches, Width 12 inches, Height 16 inches

• Length 12 inches, Width 24 inches, Height 16 inches