4-2 Synthetic Division

Front

What is synthetic division?

Back

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

Front

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing down the coefficients of the polynomial and the zero of the divisor (c) on the left.

Front

How do you find the zero of the divisor in synthetic division?

Back

To find the zero of the divisor (x - c), set x = c. For example, if the divisor is (x + 4), the zero is -4.

Front

What do you do with the leading coefficient in synthetic division?

Back

Bring down the leading coefficient of the polynomial as the first number in the synthetic division process.

Front

What is the purpose of multiplying in synthetic division?

Back

After bringing down the leading coefficient, you multiply it by the zero of the divisor and add it to the next coefficient.

Front

What does the remainder represent in synthetic division?

Back

The remainder in synthetic division represents the value of the polynomial at the zero of the divisor.

Front

How do you interpret the result of synthetic division?

Back

The result of synthetic division gives you the quotient polynomial and the remainder, which can be expressed as a fraction over the divisor.

Front

What is the relationship between synthetic division and polynomial long division?

Back

Synthetic division is a shortcut method for polynomial long division, specifically for dividing by linear factors.

Front

What is the significance of the coefficients in synthetic division?

Back

The coefficients of the polynomial are used in synthetic division to perform the calculations and determine the quotient and remainder.

Front

Can synthetic division be used for any polynomial?

Back

Synthetic division can only be used for polynomials divided by linear divisors of the form (x - c).