Factoring Polynomials and Expressions

The video tutorial demonstrates how to factor the polynomial 4y^3 + y. It begins by identifying common factors, specifically the variable y, and proceeds to factor it out, resulting in y(4y^2 + 1). The tutorial explains why the difference of squares method is not applicable and verifies the factored form by multiplying back to the original polynomial.

What is the initial polynomial expression that needs to be factored?

• 4y^3 + y

• 4y^2 + y

• 4y^3 + 1

• y^3 + 4y

What is the first step in factoring the polynomial 4y^3 + y?

• Complete the square

• Apply the difference of squares

• Factor out the common term y

• Use the quadratic formula

Which term is factored out from the polynomial 4y^3 + y?

• 1

• y

• y^2

• 4y

After factoring out the common term, what expression is left inside the parentheses?

• 4y^3 + 1

• y^2 + 4

• 4y^2 + 1

• 4y + 1

What is the common factor in the expression 4y^3 + y?

• 4

• y

• y^3

• 1

Why can't the difference of squares method be applied to 4y^2 + 1?

• Because it is a sum of squares

• Because it is already factored

• Because it is a linear expression

• Because it is a difference of cubes

What is the nature of the terms in 4y^2 + 1 that prevents using the difference of squares?

• One is a cube term

• One is a linear term

• Both are square terms

• Both are linear terms

What is the final factored form of the polynomial 4y^3 + y?

• 4(y^3 + y)

• 4y(y^2 + 1)

• y(4y^2 + 1)

• y^2(4y + 1)

How can you verify the correctness of the factored form y(4y^2 + 1)?

• By completing the square

• By applying the quadratic formula

• By multiplying back to the original polynomial

• By using the difference of squares

What should y times 4y^2 equal when verifying the factored form?

• y^3

• 4y^2

• 4y^3

• 4y