Flashcard 4.3: 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 descending order, using zero as a placeholder for any missing terms.

Front

In synthetic division, what does the left-hand box represent?

Back

The value of 'c' from the linear factor (x - c) being used for division.

Front

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

Back

It ensures that the degree of the polynomial is accurately represented, allowing for correct calculations.

Front

How do you determine the coefficients for synthetic division?

Back

List the coefficients of the polynomial in descending order of their corresponding powers.

Front

What is the remainder in synthetic division?

Back

The value left after completing the synthetic division process, representing the leftover part of the polynomial.

Front

What mistake did Cam make in his synthetic division?

Back

He did not use a zero placeholder for the x^3 term.

Front

What is the correct order of coefficients for the polynomial (3x - 4x^3 + 6x^4 + 1)?

Back

6, -4, 0, 3, 1.

Front

What term is missing in the polynomial 2x^3 + 5x^2 + 9 ÷ (x + 3)?

Back

x.

Front

How should the answer to a synthetic division problem be written?

Back

In standard polynomial form, combining like terms.