Polynomial Operations

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 - x + 7, the degree is 3.

Front

How do you simplify a polynomial expression?

Back

To simplify a polynomial expression, combine like terms by adding or subtracting their coefficients.

Tags

CCSS.7.EE.A.1

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Tags

CCSS.6.EE.A.3

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Tags

CCSS.HSA.APR.A.1

Front

What is the difference between addition and subtraction of polynomials?

Back

When adding polynomials, combine like terms. When subtracting, distribute the negative sign and then combine like terms.

Tags

CCSS.HSA.APR.A.1

Front

What is a like term in a polynomial?

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.

Tags

CCSS.6.EE.A.2B

Front

What is the process for finding the sum of two polynomials?

Back

To find the sum of two polynomials, align like terms and add their coefficients.

Tags

CCSS.HSA.APR.A.1

Front

What is the process for finding the difference of two polynomials?

Back

To find the difference, subtract the coefficients of like terms after distributing the negative sign to the second polynomial.

Tags

CCSS.HSA.APR.A.1

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, from highest to lowest.