Operations with Polynomials: Add, Subtract, & Multiply

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 the polynomial 4x^3 + 2x^2 - 5, 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) = (3 + 4)x^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 + 1) = (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by each term in a polynomial.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property or 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 that contains exactly two terms, such as x + 3 or 2x^2 - 5.

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms, such as x^2 + 5x + 6.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors. For example, x^2 - 5x + 6 can be factored as (x - 2)(x - 3).

Front

What is the result of multiplying -7x(11x + 12)?

Back

The result is -77x^2 - 84x.