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 the coefficients of the polynomial in a row and place the value of c (from x - c) to the left.

Front

What do you do with the first coefficient in synthetic division?

Back

Bring down the first coefficient unchanged.

Front

How do you handle the coefficients in synthetic division?

Back

Multiply the value of c by the number just brought down, then add it to the next coefficient.

Front

What is the remainder in synthetic division?

Back

The last number obtained after completing the synthetic division process.

Front

What does a zero placeholder represent in synthetic division?

Back

It represents a missing term in the polynomial, ensuring the correct degree is maintained.

Front

If dividing by (x - 2), what number do you use in synthetic division?

Back

You use 2 as the number in the left-hand box.

Front

What is the significance of the degree of the polynomial in synthetic division?

Back

The degree determines how many coefficients you will write and how many zero placeholders may be needed.

Front

What should you do if a polynomial is missing a term?

Back

Insert a zero as the coefficient for that term.

Front

How do you write the final answer after synthetic division?

Back

The result is written as a polynomial of one degree less than the original, followed by the remainder.