Adding, Subtracting, Multiplying, and Dividing 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. For example, 2x^2 + 3x - 5 is a polynomial.

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 - x, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2+4)x^2 + 3x + 5 = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 2x) - (x^2 + 4) = (3-1)x^2 + 2x - 4 = 2x^2 + 2x - 4.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by using the distributive property (also known as the FOIL method for binomials). For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have one or more terms. For example, 5x is a monomial, and 5x + 3 is a polynomial.

Front

How do you classify polynomials by degree?

Back

Polynomials can be classified as 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 standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^3 + 2x^2 - x + 5 is in standard form.