Adding, Subtracting, and Multiplying 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

How do you determine the number of terms in a polynomial?

Back

To determine the number of terms in a polynomial, count the distinct monomials (terms) separated by addition or subtraction.

Front

What is the degree of a polynomial?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

What are like terms in a polynomial?

Back

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

Front

How do you subtract polynomials?

Back

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

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method (First, Outside, Inside, Last).

Front

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

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial, multiplying the coefficients and adding the exponents of like bases.

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.

Front

How do you factor a polynomial?

Back

To factor a polynomial, find the greatest common factor (GCF) of the terms and use techniques such as grouping, using special products, or applying the quadratic formula if applicable.