Exploring Adding and Subtracting Polynomials

This video tutorial covers the basics of adding and subtracting polynomials. It begins with an introduction to polynomials, explaining their components such as variables and whole numbers. The tutorial then demonstrates how to add polynomials by combining like terms and performing arithmetic operations. It also covers subtracting polynomials, emphasizing the importance of distributing terms correctly. A complex example is provided to illustrate multiple polynomial operations, including handling exponents and combining terms. The video concludes with additional resources for further learning.

What is a polynomial?

• A series of numbers added together without any variables.

• A mathematical expression that includes variables raised to positive whole numbers and their coefficients.

• An equation with a single variable to the power of one.

• A function that only includes variables with negative exponents.

How do you combine like terms in a polynomial?

• By adding the exponents of the terms.

• By dividing the polynomial by the number of terms.

• By multiplying the coefficients of the terms.

• By adding the coefficients of the terms with the same variable and exponent.

What is the result of adding 4x to 6x?

• 2x

• 10

• 10x

• 24x

In polynomial operations, what does the term 'like terms' refer to?

• Terms that have the same variable but different exponents.

• Terms that have no variables.

• Terms that have different variables and different exponents.

• Terms that have the same variable and the same exponent.

What is the coefficient of x in the term 5x?

• x

• 5

• 0

• 1

What happens when you distribute a negative number across a polynomial?

• The coefficients of all terms are divided by the negative number.

• The exponents of all terms are decreased by one.

• The signs of all terms in the polynomial are reversed.

• All terms in the polynomial become positive.

When subtracting polynomials, what is the first step?

• Multiply each term by the leading coefficient.

• Distribute the subtraction across each term.

• Combine all like terms.

• Identify the highest power of the variable.

What does it mean to distribute a number across a polynomial?

• To add the number to each term of the polynomial.

• To subtract the number from each term of the polynomial.

• To multiply the number by each term of the polynomial.

• To divide each term of the polynomial by the number.

What is the result of subtracting 6x^2 from 2x^2?

• -4x^2

• 4x^2

• 8x^2

• -8x^2

How do you find the simplified form of a polynomial?

• By dividing each term by its coefficient.

• By subtracting the highest power term from the polynomial.

• By combining like terms and simplifying each operation.

• By factoring out the greatest common divisor.