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

Identify the root of the divisor (x - c), which is c.

Front

How do you set up Synthetic Division?

Back

Write the coefficients of the polynomial in a row and place the root c to the left.

Front

What do you do with the first coefficient in Synthetic Division?

Back

Bring down the first coefficient as is.

Front

What is the process after bringing down the first coefficient?

Back

Multiply the root c by the number just brought down, and write the result under the next coefficient.

Front

What do you do after writing the result under the next coefficient?

Back

Add the two numbers in that column.

Front

What is the result of Synthetic Division?

Back

The final row gives the coefficients of the quotient polynomial, and the last number is the remainder.

Front

How do you express the result of Synthetic Division?

Back

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

Front

What is the remainder theorem?

Back

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

Front

What is the significance of the remainder in Synthetic Division?

Back

The remainder indicates how much is left over after division; it can be used to evaluate the polynomial at specific points.