Adding Polynomials by Combining Like Terms

This video tutorial teaches how to add polynomials by combining like terms. It clarifies common misconceptions, such as the incorrect addition of exponents, and explains the importance of aligning terms by degree. The tutorial uses examples and algebra tiles to demonstrate the process, emphasizing that polynomial addition is closed under addition, meaning the sum of polynomials is always a polynomial. The video also highlights the differences between polynomial addition and whole number addition, particularly the absence of carrying or trading.

What is the degree of a term with an exponent of 2?

• Fourth-degree

• First-degree

• Second-degree

• Third-degree

Why can't x cubed plus x squared be simplified to x to the fifth?

• Because they are both constants

• Because they have the same exponents

• Because they involve different operations

• Because they are different variables

When adding polynomials, how should terms be aligned?

• By their coefficients

• By their constants

• By their variables

• By their degrees

What is the result of adding 5x squared and 4x squared?

• 9x squared

• 25x squared

• 1x squared

• 20x squared

Why is there no carrying or trading in polynomial addition?

• Because the variables are fixed

• Because each term is unique

• Because the terms are constants

• Because the coefficients are zero

What does closure in polynomial addition mean?

• The sum of two polynomials is always a constant

• The sum of two polynomials is always zero

• The sum of two polynomials is always an integer

• The sum of two polynomials is always a polynomial

How is closure for polynomials similar to closure for integers?

• Both result in an element of the same set

• Both result in an integer

• Both result in a polynomial

• Both result in a constant