Operations with Polynomials

Front

What is a constant monomial?

Back

A constant monomial is a polynomial that has only one term and that term is a constant (e.g., 12).

Front

How do you classify the polynomial 4x^3 - 5x^2 + 3x?

Back

This polynomial is classified as a cubic trinomial because it has a degree of 3 and three terms.

Front

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

Back

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

Front

What is the result of adding the polynomials (4x^3 - 5x^2 + 3x) and (-2x^3 - x^2 + 6x)?

Back

The result is 2x^3 - 6x^2 + 9x.

Front

What is the result of dividing the polynomial (6x^2 - 9x) by 3x?

Back

The result is 2x - 3.

Front

What is the product of (x + 2)(x + 3)?

Back

The product is x^2 + 5x + 6.

Front

How do you simplify the expression (4x^2 + x) - (x^2 + 2x)?

Back

The simplified expression is 3x^2 - x.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Front

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

Back

The leading coefficient is 5, which is the coefficient of the term with the highest degree.

Front

What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.