Operations with Polynomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 12 or 3x^2.

Front

How do you classify a polynomial by its degree?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, 3x^3 - 6x is a cubic polynomial because the highest degree is 3.

Front

What is the result of simplifying the expression -3x^2(7x^2 - x + 4)?

Back

The result is -21x^4 + 3x^3 - 12x^2.

Front

How do you simplify the expression (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

The simplified expression is 5b^4 - 2b^3 + 4.

Front

What is the product of (4x + 1)(5x - 2)?

Back

The product is 20x^2 - 3x - 2.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.

Front

What are the different classifications of polynomials based on the number of terms?

Back

Polynomials can be classified as monomials (1 term), binomials (2 terms), and trinomials (3 terms). Polynomials with more than three terms are simply called polynomials.

Front

What is the degree of the polynomial 2x^4 + 3x^2 - 5?

Back

The degree of the polynomial is 4, which is the highest exponent of the variable x.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a single term, while a polynomial can have multiple terms.