Exploring Polynomial Addition and Subtraction

This video tutorial covers polynomial operations, focusing on adding and subtracting polynomials. It begins with definitions of polynomials, terms, and like terms, and explains how to combine like terms. The tutorial then provides detailed steps and examples for adding and subtracting polynomials, emphasizing the importance of using the sign in front of terms and arranging terms in descending order.

What is a polynomial?

• An expression with only numbers

• An expression with only variables

• An expression with more than one term

• A single term expression

Which of the following is an example of a term?

• 3x^2 + 2x

• 2x

• 3 + 4

• x^2 + y^2

What are like terms?

• Terms with the same variables and exponents

• Terms with the same coefficients

• Terms with different exponents

• Terms with different variables

When combining like terms, what do you add or subtract?

• The constants

• The coefficients

• The exponents

• The variables

What is the first step in adding polynomials?

• Multiply the terms

• Distribute the coefficients

• Drop down all terms without parentheses

• Combine like terms

In the example 6p + 5 + 7p + 4, what is the result after combining like terms?

• 6p + 7p + 5 + 4

• 13p + 5

• 6p + 7p + 9

• 13p + 9

What is the first step in subtracting polynomials?

• Distribute the coefficients

• Combine like terms

• Drop down the first parentheses as is

• Multiply the terms

In the example 2 + 7x + 7x^3 - 3x^4 + 5x^3 + 3, what is the result after distributing the negative sign and combining like terms?

• 2 + 7x + 7x^3 - 3x^4 - 5x^3 + 3

• 2 + 7x + 7x^3 - 3x^4 + 5x^3 - 3

• 2 + 7x + 7x^3 - 3x^4 - 5x^3 - 3

• 2 + 7x + 7x^3 - 3x^4 + 5x^3 + 3

What is the result of combining 5x^3 + 2x^4 + x - 6x^3 - x^4 + 6x?

• 3x^4 - x^3 + 5x

• 5x^3 - 6x^3 + 2x^4 - x^4 + x + 6x

• 3x^4 - x^3 - 5x

• 5x^3 + 2x^4 + x - 6x^3 - x^4 + 6x

What is the final step in both adding and subtracting polynomials?

• Multiply the terms

• Drop down all terms without parentheses

• Distribute the coefficients

• Combine like terms