Adding and Subtracting Polynomials Explained

The video tutorial introduces polynomials, explaining their structure and key features such as positive integer exponents and variable coefficients. It covers essential vocabulary like degree and leading coefficient. The tutorial then demonstrates how to add and subtract polynomials by combining like terms, emphasizing the importance of handling negative signs correctly.

What must the exponents in a polynomial be?

• Positive integers

• Positive and negative integers

• Negative integers

• Any real numbers

What is the term called that has no variable in a polynomial?

• Variable term

• Leading term

• Constant term

• Coefficient

How is the degree of a polynomial determined?

• By adding all the exponents

• By the coefficient with the highest value

• By the highest exponent in the polynomial

• By the number of terms in the polynomial

What is the leading coefficient of a polynomial?

• The coefficient of the first term when arranged in ascending order

• The coefficient of the term with the lowest exponent

• The constant term of the polynomial

• The coefficient of the term with the highest exponent

When adding polynomials, what must you do with the terms?

• Combine like terms

• Subtract like terms

• Divide like terms

• Multiply like terms

What happens if a term in one polynomial doesn't have a matching term in the polynomial it's being added to?

• It's removed from the equation

• It's multiplied by 2

• It's converted into a constant term

• It remains unchanged in the sum

How do you handle negative signs when adding polynomials?

• Ignore them

• Distribute them across all terms

• Only apply them to the first term

• Convert them to positive signs

What is the first step in subtracting polynomials?

• Combine like terms immediately

• Distribute the negative sign across the terms being subtracted

• Convert all terms to positive

• Rearrange the polynomials in descending order

What does distributing the negative sign in polynomial subtraction achieve?

• It converts all coefficients to negative

• It simplifies the polynomial to a single term

• It ensures correct subtraction of like terms

• It eliminates the constant term

What should you pay attention to when subtracting polynomials?

• The number of terms in the polynomial

• The degree of the polynomial

• Negative signs and their distribution

• The leading coefficient