3.6 Long and Synthetic Division of Polynomials

Front

What is long division of polynomials?

Back

A method used to divide a polynomial by another polynomial of lower degree, similar to long division with numbers.

Front

What is synthetic division?

Back

A simplified form of polynomial division that is used when dividing by a linear factor, making calculations easier.

Front

What is a polynomial?

Back

An expression consisting of variables raised to non-negative integer powers and coefficients, e.g., 2x^3 + 3x^2 - 5.

Front

What is a divisor in polynomial division?

Back

The polynomial by which another polynomial is divided.

Front

What is a quotient in polynomial division?

Back

The result obtained from dividing one polynomial by another.

Front

What is a remainder in polynomial division?

Back

The amount left over after dividing one polynomial by another, which cannot be divided by the divisor.

Front

How do you perform long division of polynomials?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat with the new polynomial.

Front

What is the first step in synthetic division?

Back

Identify the zero of the divisor (for x - c, use c) and set up the synthetic division table.

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

To maintain the correct degree of the polynomial when a term is missing, ensuring accurate calculations.

Front

What is the leading coefficient of a polynomial?

Back

The coefficient of the term with the highest degree in the polynomial.