Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c) using coefficients.

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 of the degree.

Front

When dividing by (x - c), what value of c is used in synthetic division?

Back

The value of c used is the opposite sign of the constant in the factor (x - c). For (x - 2), c = 2.

Front

What is a zero placeholder in synthetic division?

Back

A zero placeholder is used to represent missing terms in the polynomial when setting up synthetic division, ensuring all degrees are accounted for.

Front

How do you determine the number of zero placeholders needed?

Back

The number of zero placeholders needed corresponds to the degree of the polynomial minus the number of non-zero terms.

Front

What is the remainder in synthetic division?

Back

The remainder is the last number obtained in the synthetic division process, representing what is left after division.

Front

How do you interpret the result of synthetic division?

Back

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

Front

What is the significance of the leading coefficient in synthetic division?

Back

The leading coefficient affects the degree and the shape of the resulting polynomial after division.

Front

What happens if you forget to use a zero placeholder?

Back

Forgetting a zero placeholder can lead to incorrect calculations and an inaccurate quotient.

Front

How do you set up synthetic division for (2x^3 - 5x^2 + 3x + 7) ÷ (x - 2)?

Back

Write the coefficients [2, -5, 3, 7] and use 2 as the value for synthetic division.