Polynomial Operations and Exponent Rules

George Woodbury from the College of the Seoa in Velia, California, provides a comprehensive review of exponent rules and polynomial operations. The video covers simplifying expressions, handling fractional and negative exponents, and performing polynomial operations such as addition, subtraction, multiplication, and long division. Key rules like the product and quotient rules are explained, along with strategies for dealing with negative exponents and polynomial division.

When simplifying expressions with exponents, how should coefficients be treated?

• Add them together

• Subtract them

• Multiply them

• Divide them

What is the quotient rule for exponents?

• Subtract the exponent in the denominator from the exponent in the numerator

• Multiply the exponents of like bases

• Divide the exponents of like bases

• Add the exponents of like bases

How should negative exponents be handled in an expression?

• Leave them as they are

• Multiply them by -1

• Move the base with the negative exponent to the denominator

• Add a positive number to them

What happens when you raise a product to an exponent?

• The exponent is subtracted from each base

• The exponent is added to each base

• Each base in the product is raised to the exponent

• Only the first base is raised to the exponent

In polynomial addition, what is the key step?

• Change the sign of the second polynomial

• Combine like terms

• Multiply the polynomials

• Divide the polynomials

What is the first step in polynomial subtraction?

• Multiply the polynomials

• Distribute the negative sign to each term in the second polynomial

• Add the polynomials

• Combine like terms

When multiplying polynomials, what method is often used?

• FOIL method

• Quotient rule

• Addition of coefficients

• Negative exponent rule

In polynomial division, what should you do if a term is missing in the dividend?

• Subtract the missing term

• Multiply the missing term by zero

• Add a placeholder for the missing term

• Ignore the missing term

What is the purpose of changing signs during polynomial division?

• To cancel out terms

• To simplify the expression

• To multiply terms

• To add terms together

How is the remainder expressed in polynomial division?

• As a fraction over the divisor

• As a negative number

• As a positive number

• As a separate term