Polynomial Division and Remainder Flashcard

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers. It results in a quotient and a remainder.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by a linear divisor (x - c) is equal to f(c).

Front

How do you divide a polynomial by a binomial?

Back

To divide a polynomial by a binomial, use long division or synthetic division to find the quotient and remainder.

Front

What is the quotient in polynomial division?

Back

The quotient is the result of dividing one polynomial by another, representing how many times the divisor fits into the dividend.

Front

What is a remainder in polynomial division?

Back

The remainder is what is left over after dividing a polynomial by another polynomial when the division is not exact.

Front

Divide: 3x^2 - 8x + 6 by (x - 1). What is the result?

Back

3x^2 - 2x - 2 + (-4)/(x - 1)

Front

Divide: x^3 - 6x^2 + 11x - 6 by (x - 2). What is the result?

Back

x^2 - 4x + 3

Front

Divide: 8x^4 - 4x^3 by 4x^2. What is the result?

Back

2x^2 - x

Front

Divide: x^3 + 4x^2 + 5x + 6 by (x + 3). What is the result?

Back

x^2 + x + 2

Front

Find the remainder when x^4 - 2x^3 + 3x - 4 is divided by (x - 2).

Back

The remainder is 2.