Add and Subtract Polynomials

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, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (5x^2 - 3) - (2x^2 + 4) = 5x^2 - 3 - 2x^2 - 4 = 3x^2 - 7.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms. For example, 2x^2 + 3x + 1 is a trinomial.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms. For example, 5x (monomial), 3x + 2 (binomial), and x^2 + 2x + 1 (trinomial).

Front

How do you classify polynomials by their degree?

Back

Polynomials can be classified as constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), quartic (degree 4), and so on, based on the highest degree of their terms.

Front

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

Back

The result is (2x^2 + 3) + (4x^2 - 5) = 6x^2 - 2.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means to combine like terms and reduce the expression to its simplest form.