Adding, Subtracting, Multiplying, and Dividing Polynomials

Front

Define 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

What is the degree of a polynomial?

Back

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

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.

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

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 polynomial.

Front

What is the result of multiplying (a + b)(a - b)?

Back

The result is a^2 - b^2, which is the difference of squares.

Front

Find the difference: (4n - 3n^3) - (3n^3 + 4n).

Back

-6n^3.

Front

Find the product: (b + 3)(b^2 + 2b + 1).

Back

b^3 + 5b^2 + 7b + 3.