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 the coefficients: [4, 4, -9, -1, 2] and the root 1.

Front

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

Back

Bring down the first coefficient as is.

Front

In synthetic division, what do you do after bringing down the first coefficient?

Back

Multiply the root (c) by the number just brought down and write the result under the next coefficient.

Front

What is the result of the synthetic division of 4x^4 + 4x^3 - 9x^2 - x + 2 by (x - 1)?

Back

4x^3 + 8x^2 - x - 2.

Front

What is the remainder in synthetic division?

Back

The last number obtained after completing the synthetic division process.

Front

How do you express the result of synthetic division?

Back

The result is expressed as the quotient plus the remainder over the divisor.

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

What is the proper way to write the answer for the division of 2x^3 - x^2 - 25x - 12?

Back

2x^3 - x^2 - 25x - 12.