Exploring Polynomial Addition and Subtraction

This video tutorial covers the basics of polynomials, including definitions of monomials, binomials, and trinomials. It explains how to write polynomials in standard form by ordering terms based on their exponents. The tutorial also discusses classifying polynomials by degree and number of terms. Practice problems are provided to reinforce these concepts. Additionally, the video demonstrates how to add and subtract polynomials by combining like terms and using distribution.

What is a monomial?

• A polynomial with two terms

• A polynomial with three terms

• A single term expression

• A constant term

Which of the following is a polynomial in standard form?

• 3x^2 + 2x + 4

• 2x^2 + 4 + 3x

• 4 + 3x^2 + 2x

• 2x + 3x^2 + 4

What is the degree of the polynomial 5x^3 + 2x^2 + x + 7?

• 3

• 2

• 4

• 1

How many terms does a binomial have?

• One

• Four

• Two

• Three

Which of the following is a trinomial?

• x^3 + x^2

• x^2 + 2x + 1

• x^4 + x^3 + x^2 + x

• x + 1

What is the result of adding 3x^2 + 2x + 1 and 4x^2 + x + 5?

• 7x^2 + 2x + 6

• 7x^2 + x + 6

• 7x^2 + 3x + 4

• 7x^2 + 3x + 6

When adding polynomials, what must be true about the terms you combine?

• They must have the same coefficient

• They must have the same variable and exponent

• They must have the same constant term

• They must have the same degree

What is the result of subtracting (5x^2 + 3x + 2) from (7x^2 + 4x + 5)?

• 2x^2 + x + 1

• 2x^2 + x + 3

• 12x^2 + 7x + 7

• 2x^2 + x + 7

What is the first step in subtracting polynomials?

• Add the coefficients

• Distribute the negative sign

• Multiply the constants

• Combine like terms

What is the simplified form of (3x^2 + 2x - 1) - (x^2 - x + 4)?

• 2x^2 + 3x - 5

• 2x^2 + 3x + 3

• 4x^2 + x - 5

• 2x^2 + x - 5