5.4B Synthetic Division

Front

What is synthetic division?

Back

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

Front

When is (x - c) a factor of a polynomial?

Back

(x - c) is a factor of a polynomial if the polynomial evaluates to zero at x = c.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

Front

How do you determine if (x - 1) is a factor of a polynomial?

Back

Evaluate the polynomial at x = 1. If the result is 0, then (x - 1) is a factor.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial being divided.

Front

What do you do with the divisor in synthetic division?

Back

Use the root of the divisor (c from (x - c)) as the number to bring down in synthetic division.

Front

What is the purpose of bringing down the first coefficient in synthetic division?

Back

It starts the synthetic division process and allows for further calculations.

Front

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

Back

Multiply the root of the divisor by the coefficient just brought down and add it to the next coefficient.

Front

What does the last number in synthetic division represent?

Back

The last number represents the remainder of the division.

Front

If the remainder is zero, what can be concluded?

Back

If the remainder is zero, then the divisor is a factor of the polynomial.