Adding, Subtracting, Multiplying, and Dividing Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication. Example: 3x^2 + 2x - 5.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power. Example: (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves distributing the negative sign and then combining like terms. Example: (5x^2 + 3) - (2x^2 + 4) = 3x^2 - 1.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second. Example: (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6.

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

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. Example: In 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What is the process for dividing polynomials?

Back

Dividing polynomials involves using long division or synthetic division to simplify the expression. Example: To divide 6x^2 + 12x by 3x, the result is 2x + 4.

Front

What are like terms?

Back

Like terms are terms in a polynomial 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.

Front

What is the result of (x^5 + x^3) - (6x - x^3 + 6x^5)?

Back

The result is -5x^5 + 2x^3 - 6x.

Front

How do you simplify (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3)?

Back

The simplified result is -2x^3 + x^2 + 1.