Synthetic Division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear binomial of the form (x - c) without using long division.

Front

How many zeros are needed in the top row for synthetic division of x^6 + 4x^3 + 2?

Back

4 zeros are needed.

Front

What is the first step in synthetic division?

Back

Set up the synthetic division by writing the coefficients of the polynomial.

Front

What is the quotient of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

2x^2 - x + 3.

Front

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

Back

Multiply the divisor (c) by the number just brought down.

Front

What is the purpose of synthetic division?

Back

To simplify the process of dividing polynomials and to find the quotient and remainder.

Front

What is the next step after multiplying in synthetic division?

Back

Add the result to the next coefficient.

Front

What does it mean if the remainder is zero in synthetic division?

Back

It means that the divisor is a factor of the polynomial.

Front

What is the result of dividing x^3 + 2x^2 - 5 by (x - 1) using synthetic division?

Back

The quotient is x^2 + 3x - 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.