Polynomial Mini Flashcard

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. It can be written 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 are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 3x^4 + 2x^3 - x + 5, the degree is 4.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^2 and -3 are monomials.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, x + 5 and 3x^2 - 2 are binomials.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the FOIL method: First, Outside, Inside, Last. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial. It involves dividing the leading terms, multiplying, and subtracting until the remainder is of lower degree.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder is f(c).