Adding Polynomials: Key Concepts and Techniques

This video tutorial covers the basics of adding polynomials, focusing on identifying like terms and combining them. It explains the concept of like terms, which have the same base and exponent, and provides examples to illustrate this. The tutorial then outlines the steps for adding polynomials, including combining like terms and writing the result in standard form. Several examples are provided to demonstrate these steps, including handling polynomials with parentheses. The video aims to help students understand how to add polynomials effectively.

What must be true for terms to be considered like terms?

• They must have the same constant.

• They must have the same variable.

• They must have the same base and exponent.

• They must have the same coefficient.

Why are 7x and 7x^2 not considered like terms?

• They have different variables.

• They have different coefficients.

• They have different exponents.

• They have different bases.

Which of the following pairs are like terms?

• 9y and 3

• 7x and 7x^2

• 2x^2 and 6x^2

• 5 and 10x

What is the first step in adding polynomials?

• Multiply the coefficients.

• Combine like terms.

• Subtract the exponents.

• Divide the constants.

How do you write the final answer when adding polynomials?

• In ascending order of exponents.

• In descending order of exponents.

• In alphabetical order of variables.

• In any order.

What is the result of combining 7x + 3x?

• 7x^3

• 10x

• 4x

• 10x^2

What is the sum of 4x^2 and x^2?

• 4x^3

• x^4

• 3x^2

• 5x^2

What is the result of adding -12x and x?

• 12x

• 11x

• -13x

• -11x

When adding polynomials with parentheses, what should you check first?

• If there are any like terms.

• If the coefficients are the same.

• If the exponents are the same.

• If there is anything to distribute.

What is the result of combining 9x^2 and x^2?

• 9x^3

• x^4

• 10x^2

• 8x^2