Adding, Subtracting, & Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, 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 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, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 - 3) - (2x^2 + 1) = 3x^2 - 4.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 - 2x^2 + x is in standard form.

Front

What are like terms?

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.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 3x(2x^2 + x) = 6x^3 + 3x^2.

Front

What is the result of multiplying (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6, obtained by using the distributive property.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 5 or 3x^2 - 2.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms, such as x^2 + 3x + 2.