Unit 6.1 & 6.2 Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

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 - 2x^2 + x, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms. For example, x^2 + 2x + 1 is a trinomial.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 3x(4x^2 - x - 3) = 12x^3 - 3x^2 - 9x.

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. For example, in -2x^5 + 3x - 1, the leading coefficient is -2.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (x^3 + 6x - 5) + (-6x^2 + 4x + 3) = x^3 - 6x^2 + 10x - 2.

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero. For example, the roots of y = (x + 4)(x - 3)(x - 8) are -4, 3, and 8.

Front

What is a 5th degree polynomial?

Back

A 5th degree polynomial is a polynomial where the highest power of the variable is 5. For example, -2x^5 + 3x - 1 is a 5th degree polynomial.