Understanding Polynomials

The video introduces polynomials, starting with monomials and expanding to binomials and trinomials. It explains key characteristics like degree, standard form, and leading coefficient. The video then demonstrates how to add and subtract polynomials by combining like terms and distributing negatives, respectively.

What is a monomial?

• A single number, variable, or product of numbers and variables with whole number exponents

• A polynomial with three terms

• A polynomial with two terms

• A sum of variables and numbers

Which of the following is a binomial?

• 7x

• 8x^3

• x + 7

• 5x^2 + 3x + 1

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

• 3

• 4

• 2

• 1

What does it mean for a polynomial to be in standard form?

• The terms are arranged in increasing order of exponents

• The terms are arranged in alphabetical order

• The terms are arranged in random order

• The terms are arranged in decreasing order of exponents

What is the leading coefficient of the polynomial -x^3 + 15x + 3?

• 3

• 0

• -1

• 15

When adding polynomials, what is the main step involved?

• Multiplying like terms

• Subtracting like terms

• Dividing like terms

• Adding like terms

In the expression 2x^3 + x^3, what is the result of combining like terms?

• 2x^6

• x^6

• 3x^3

• x^3

What is the first step in subtracting polynomials?

• Divide the polynomials

• Multiply the polynomials

• Distribute the negative sign

• Add the polynomials

After distributing the negative sign in subtraction, what should you do next?

• Divide the polynomials

• Multiply the polynomials

• Combine like terms

• Add the polynomials

What is the result of subtracting 4n^2 + 5 from -2n^2 + 2n - 4?

• 4n^2 + 2n + 9

• 6n^2 + 2n + 9

• 2n^2 - 2n + 9

• 6n^2 - 2n + 9