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

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing the coefficients of the polynomial in a row and the zero of the divisor (c from x - c) to the left.

Front

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

Back

If the divisor is (x - c), the zero is simply c. For example, for (x - 2), the zero is 2.

Front

What do you do with the coefficients during synthetic division?

Back

You bring down the leading coefficient and then multiply it by the zero of the divisor, adding the result to the next coefficient.

Front

What is the result of synthetic division?

Back

The result of synthetic division is a polynomial of one degree less than the original polynomial, along with a remainder.

Front

How do you express the remainder in synthetic division?

Back

The remainder is expressed as a fraction over the divisor. For example, if the remainder is r and the divisor is (x - c), it is expressed as r/(x - c).

Front

What is the significance of the coefficients in synthetic division?

Back

The coefficients represent the values of the polynomial at different powers of x, and they are used to perform the calculations in synthetic division.

Front

If dividing 2x^3 - 5x - 7 by (x - 2), what is the first coefficient to bring down?

Back

The first coefficient to bring down is 2, which is the coefficient of x^3.

Front

In synthetic division, what happens if a coefficient is missing?

Back

If a coefficient is missing, it is represented as 0 in the synthetic division setup.

Front

What is the final form of the answer after synthetic division?

Back

The final answer is written as the quotient polynomial plus the remainder over the divisor.