Synthetic Division

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear factor 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 and the zero of the divisor (c) on the left.

Front

How do you determine the zero of the divisor in synthetic division?

Back

If the divisor is (x - c), then the zero is c.

Front

What do you do after bringing down the first coefficient in synthetic division?

Back

Multiply the number you just brought down by the zero of the divisor and write the result under the next coefficient.

Front

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

Back

To account for missing degrees in the polynomial, ensuring the correct alignment of coefficients.

Front

How do you find the remainder in synthetic division?

Back

The last number obtained after completing the synthetic division process is the remainder.

Front

What is the significance of the coefficients in synthetic division?

Back

They represent the values of the polynomial at different degrees, which are used in the division process.

Front

What happens if you forget to use a zero placeholder in synthetic division?

Back

It can lead to incorrect calculations and an inaccurate result.

Front

In synthetic division, what do you do with the remainders?

Back

The remainders can be expressed as a fraction over the divisor or added to the quotient.

Front

What is the result of dividing a polynomial by a linear factor?

Back

The result is a polynomial of one degree less than the original polynomial, plus a remainder.