Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Example: 2x^2 + 3x - 5.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Example: (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Tags

CCSS.HSA.APR.A.1

Front

How do you subtract polynomials?

Back

Subtracting polynomials involves distributing the negative sign and then combining like terms. Example: (3x^2 + 2x) - (x^2 + 4) = 2x^2 + 2x - 4.

Tags

CCSS.HSA.APR.A.1

Front

What is the process of expanding a polynomial?

Back

Expanding a polynomial means multiplying out the terms to eliminate parentheses. Example: (x + 2)(x + 3) = x^2 + 5x + 6.

Tags

CCSS.HSA.APR.A.1

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. Example: 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Tags

CCSS.6.EE.A.2B

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. Example: In 4x^3 + 2x^2 - x, the degree is 3.

Front

How do you multiply 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. Example: (x + 1)(x + 2) = x^2 + 3x + 2.

Tags

CCSS.HSA.APR.A.1

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. Example: 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. Example: x^2 + 5x + 6 is a trinomial.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term. Example: 5x^2 is a monomial, while 2x^2 + 3x is a polynomial.