Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number exponents and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 3x^2 - 2, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. Like terms are terms that have the same variable raised to the same power.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same exponent. For example, 3x^2 and 5x^2 are like terms.

Front

Simplify: (4x - 2x^3) + (5x^3 - 4x + 5)

Back

3x^3 + 5.

Front

What is the result of adding (3 - 2x + 2x^2) and (4x - 5 + 3x^2)?

Back

5x^2 + 2x - 2.

Front

How do you multiply polynomials?

Back

To multiply 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.

Front

What is the product of (x - 3) and (x^2 + 2x + 7)?

Back

x^3 - x^2 + x - 21.

Front

Simplify: 2x(-2x - 3)

Back

-4x^2 - 6x.

Front

What is the result of multiplying (3x - 2) and (6x + 1)?

Back

18x^2 - 9x - 2.