Synthetic Division Practice

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

What is the first step in synthetic division?

Back

Identify the zero of the divisor (x - c), which is c.

Front

In synthetic division, what do you place in the left-hand box?

Back

The zero of the divisor, which is the value of c.

Front

What do you do with the coefficients of the polynomial in synthetic division?

Back

Write them in a row to the right of the left-hand box.

Front

What is the role of the first coefficient in synthetic division?

Back

It is brought down unchanged to start the synthetic division process.

Front

How do you calculate the next value in synthetic division?

Back

Multiply the value in the left-hand box by the number just brought down, then add it to the next coefficient.

Front

What does the final row of numbers represent in synthetic division?

Back

The coefficients of the quotient polynomial and the remainder.

Front

How do you express the result of synthetic division?

Back

As a polynomial in descending order of degree, plus the remainder over the divisor.

Front

What happens if a coefficient is missing in the polynomial during synthetic division?

Back

You must place a zero as a placeholder for that missing coefficient.

Front

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

Back

2x^2 - x + 3.