Classifying, Adding, Subtracting, Multiplying 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 + 7, the degree is 3.

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms. For example, x^2 + 4x - 3 is a trinomial.

Front

What is a binomial?

Back

A binomial is a polynomial that consists of two terms. For example, 3x + 5 is a binomial.

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 by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 3) = 7x^2 + 2x + 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, subtract the coefficients of like terms. For example, (5x^3 + 2x) - (3x^3 + x) = 2x^3 + x.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property (FOIL method). For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c. For example, x^2 + 4x - 3 is a quadratic polynomial.

Front

What is the result of multiplying (5x + 2)(x^2 - 3x + 6)?

Back

The result is 5x^3 - 13x^2 + 24x + 12.