Polynomial Division and Remainder Flashcard

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial or monomial, similar to numerical division.

Front

What is the Remainder Theorem?

Back

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

Front

How do you divide a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 3x^2 or -5.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as x + 1 or 3x^2 - 2.

Front

What is the first step in polynomial long division?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

What do you do after dividing the leading terms in polynomial long division?

Back

After dividing, multiply the entire divisor by the result and subtract it from the dividend.

Front

What is the purpose of synthetic division?

Back

Synthetic division is a simplified method for dividing polynomials, particularly useful when dividing by linear factors.

Front

How do you find the quotient in polynomial division?

Back

The quotient is found by performing the division process and collecting the results of each step.

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of a polynomial determines the highest power of the variable and influences the division process.