Synthetic Division

Front

What is Synthetic Division?

Back

A method for dividing 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 in descending order.

Front

How do you determine the number to use in Synthetic Division?

Back

Use the value of c from the divisor (x - c). For (x - 2), use 2.

Front

What is the purpose of Synthetic Division?

Back

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

Front

Perform Synthetic Division: 4x^4 + 4x^3 - 9x^2 - x + 2 ÷ (x - 1)

Back

4x^3 + 8x^2 - x - 2.

Front

Perform Synthetic Division: 3x^3 + 5x - 1 ÷ (x + 1)

Back

3x^2 - 3x + 8 - 9/(x + 1).

Front

Perform Synthetic Division: 2x^3 + 5x^2 + 9 ÷ (x + 3)

Back

2x^2 - x + 3.

Front

What do you do with the remainder in Synthetic Division?

Back

The remainder is added to the result as a fraction over the divisor.

Front

Perform Synthetic Division: 2x^3 - 5x^2 + 3x + 7 ÷ (x - 2)

Back

2x^2 - x + 1 + 9/(x - 2).

Front

What is the significance of the coefficients in Synthetic Division?

Back

They represent the values of the polynomial at different powers of x.