Polynomials: Classifying, Adding, Subtracting

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.

Front

What is a cubic binomial?

Back

A cubic binomial is a polynomial of degree three that consists of two terms. For example, x^3 + 2 is a cubic binomial.

Front

What is a quadratic trinomial?

Back

A quadratic trinomial is a polynomial of degree two that consists of three terms. For example, x^2 + 3x + 2 is a quadratic trinomial.

Front

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

Back

It is classified as a quartic polynomial because the highest degree is four.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 + 1, the degree is 3.

Front

What is the sum of (3 - 2x + 2x^2) + (4x - 5 + 3x^2)?

Back

The sum is 5x^2 + 2x - 2.

Front

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

Back

The result is 2x^2 + x - 10.

Front

What is a quintic polynomial?

Back

A quintic polynomial is a polynomial of degree five. For example, x^5 + 2x^4 - x + 7 is a quintic polynomial.

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 2) = 6x^2 + 3x + 2.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4) - (x^2 + 2) = 2x^2 + 2.