Synthetic Division

Front

What is Synthetic Division?

Back

A method used to divide a polynomial by a linear divisor of the form (x - c) without using long division.

Front

What is the first step in Synthetic Division?

Back

Write down the coefficients of the polynomial to be divided.

Front

How do you set up Synthetic Division for (2x^3 + 7x^2 - 6x - 8) ÷ (x + 4)?

Back

Use -4 as the divisor and the coefficients 2, 7, -6, -8.

Front

What is the result of (2x^3 + 7x^2 - 6x - 8) ÷ (x + 4)?

Back

2x^2 - x - 2.

Front

What is the Remainder Theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How do you find the remainder using Synthetic Division?

Back

Evaluate the polynomial at the value of the divisor (c) after performing Synthetic Division.

Front

What is the significance of the coefficients in Synthetic Division?

Back

They represent the terms of the polynomial in descending order of degree.

Front

What is the final result format of Synthetic Division?

Back

The result is expressed as a polynomial plus a remainder over the divisor.

Front

How do you handle a negative divisor in Synthetic Division?

Back

Use the opposite sign of the divisor when setting up the Synthetic Division.

Front

What is the purpose of Synthetic Division?

Back

To simplify the process of polynomial division, making it faster and easier.