Learn how to factor out a variable from a binomial expression

The video tutorial demonstrates how to factor the polynomial 4y^3 + y. It begins by identifying common factors, specifically focusing on the common factor 'y'. The process involves factoring out 'y' to simplify the expression to 4y^2 + 1. The tutorial also addresses common misconceptions, such as mistaking the expression for a difference of squares. Finally, it verifies the factored form by multiplying back to ensure accuracy, concluding with the correct factored form of the polynomial.

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

• Look for a difference of squares

• Identify and factor out common terms

• Multiply the terms together

• Add a constant to the polynomial

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

• y^3

• 1

• 4y^2

• y

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

• 4y^2 + 1

• 4y^3 + y

• y^2 + 4

• y^3 + 4

Why can't the expression 4y^2 + 1 be factored as a difference of squares?

• It has no common terms

• It is a sum of squares, not a difference

• It is not a polynomial

• It is already in simplest form

How can you verify that the polynomial has been factored correctly?

• By dividing the polynomial by the common term

• By multiplying the factored terms to see if they give the original polynomial

• By checking if the terms are in alphabetical order

• By adding a constant to the result