Adding and Subtracting Rational Expressions

Mr. Winn's video tutorial covers operations with polynomials, including adding, subtracting, and multiplying them. It begins with definitions of monomials and polynomials, followed by an explanation of the degree of polynomials. The video then delves into exponent rules, providing examples and techniques for handling exponents in polynomial expressions. The tutorial also covers adding and subtracting polynomials, emphasizing the importance of combining like terms. Finally, it explains methods for multiplying polynomials, including the FOIL method, and provides examples to illustrate these concepts.

What is a monomial?

• An expression with two or more terms.

• A single number, variable, or product of variables with non-negative exponents.

• An expression with a negative exponent.

• A polynomial with three terms.

Which of the following is an example of a polynomial?

• 6y

• 2a^5 * b^7

• x + 5

• 5

How do you determine the degree of a polynomial?

• By adding all the exponents in the polynomial.

• By finding the highest exponent of a variable in the polynomial.

• By counting the number of terms in the polynomial.

• By multiplying the coefficients of the terms.

What is the degree of the term 2a^5 * b^7?

• 7

• 5

• 2

• 12

What is the result of any number raised to the zero power?

• 1

• Undefined

• 0

• The number itself

What is the product of 3^2 * 3^4?

• 9^8

• 3^6

• 3^8

• 9^6

What should you do if you get a negative exponent in your final answer?

• Add 1 to the exponent.

• Leave it as it is.

• Make it a fraction and flip it to the other side.

• Subtract 1 from the exponent.

When adding polynomials, what should you do with the exponents?

• Keep them the same.

• Multiply them.

• Subtract them.

• Add them together.

What is the result of (3m + 4n)^2?

• 9m^2 + 16n^2

• 9m^2 + 24mn + 16n^2

• 3m^2 + 4n^2

• 3m^2 + 8mn + 4n^2

What is the degree of the polynomial 3x^2 - 6x + 4?

• 3

• 0

• 1

• 2