Polynomial Operations and Simplifications

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 is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

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.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms.

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power.

Front

What is the process of multiplying polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in one polynomial by each term in the other.

Front

What is the result of multiplying a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial.

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 multiple terms.

Front

What is the factorization of a polynomial?

Back

Factorization of a polynomial is the process of breaking it down into simpler polynomials that, when multiplied together, give the original polynomial.