Flashcard 4.3: 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

Identify the zero of the divisor (x - c), which is c.

Front

How do you set up synthetic division?

Back

Write the coefficients of the polynomial in a row, and place the zero (c) to the left.

Front

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

Back

Bring down the first coefficient as is.

Front

What is the process after bringing down the first coefficient?

Back

Multiply the first coefficient by c and add it to the next coefficient.

Front

What do you do with the result of the addition in synthetic division?

Back

Repeat the multiplication and addition process for all coefficients.

Front

What does the last number in synthetic division represent?

Back

The remainder of the division.

Front

How do you write the result of synthetic division?

Back

The result is written as a polynomial of one degree less than the original polynomial, plus the remainder over the divisor.

Front

What is the significance of placing zeros in synthetic division?

Back

Zeros are used to represent missing degrees in the polynomial when coefficients are absent.

Front

If dividing 2x^3 + 5x^2 + 9 by (x + 3), what is the missing term?

Back

x.