Synthetic Division

Front

What is Synthetic Division?

Back

A method used to divide a polynomial by a linear divisor of the form (x - c) without using long division.

Front

What is the first step in Synthetic Division?

Back

Write down the coefficients of the polynomial in descending order of degree.

Front

How do you set up the synthetic division for the polynomial 4x^4 + 4x^3 - 9x^2 - x + 2 divided by x - 1?

Back

Use 1 (the root of x - 1) and the coefficients: 4, 4, -9, -1, 2.

Front

What does the remainder represent in Synthetic Division?

Back

The remainder is the value of the polynomial at the root used for division.

Front

How do you find the quotient in Synthetic Division?

Back

The quotient is formed by the coefficients obtained during the synthetic division process.

Front

What is the significance of the number of zeros in Synthetic Division?

Back

The number of zeros corresponds to the degree of the polynomial minus the degree of the divisor.

Front

Perform Synthetic Division: x^3 - 3x^2 - 10x + 24 ÷ (x + 3). What is the result?

Back

x^2 - 6x + 8.

Front

What is the result of dividing -2x^2 + 4x + 48 by x + 4?

Back

-2x + 12.

Front

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

Back

2x^2 - x + 1 + 9/(x - 2).

Front

How do you determine the number of zeros needed for synthetic division of x^6 + 4x^3 + 2?

Back

Count the missing degrees: 6 (degree of x^6) - 2 (degree of x^3) = 4 zeros.