Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster and requires less writing than long division.

Front

How do you set up synthetic division?

Back

To set up synthetic division, write the coefficients of the polynomial in a row. If the polynomial is missing any degrees, use 0 as the coefficient for those degrees.

Front

What do you do with the number in the left-hand box during synthetic division?

Back

The number in the left-hand box is the value of 'c' from the divisor (x - c). It is used to perform the synthetic division process.

Front

How many zeros do you need in the top row for synthetic division of x^6 + 4x^3 + 2?

Back

You need 4 zeros in the top row.

Front

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

Back

The result is 2x^2 - x + 3.

Front

What is the result of (2x^3 - 5x - 7) ÷ (x - 2)?

Back

The result is 2x^2 + 4x + 3 - 1/(x - 2).

Front

What is the first step in synthetic division?

Back

The first step is to write down the coefficients of the polynomial in descending order.

Front

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

Back

If a term is missing, you replace its coefficient with 0.

Front

What is the purpose of synthetic division?

Back

The purpose of synthetic division is to divide polynomials quickly and efficiently, especially when the divisor is a linear polynomial.

Front

Can synthetic division be used for divisors other than linear binomials?

Back

No, synthetic division is specifically designed for dividing by linear binomials of the form (x - c).