Synthetic Division

Front

What is synthetic division?

Back

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

Front

How do you set up synthetic division?

Back

Write the coefficients of the polynomial in a row, and use the zero of the divisor (c) to perform the division.

Front

What do you do if a polynomial is missing a term?

Back

You must place a zero as a coefficient for that missing term.

Front

If dividing x^6 + 4x^3 + 2, how many 0's are needed in synthetic division?

Back

4 zeros are needed for the missing x^5, x^4, x^2, and x^1 terms.

Front

What is the result of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

The result is 2x^2 - x + 3.

Front

What does it mean for k = 9 to be a zero of the function f(x) = 4x^2 - 33x - 27?

Back

It means that f(9) = 0, indicating that (x - 9) is a factor of the polynomial.

Front

What is the first step in synthetic division?

Back

Identify the zero of the divisor (x - c) and write it to the left.

Front

What is the purpose of synthetic division?

Back

To simplify the process of dividing polynomials and to find polynomial roots.

Front

What is the relationship between synthetic division and polynomial roots?

Back

If synthetic division results in a remainder of 0, then the divisor (x - c) is a factor of the polynomial.

Front

What is the format of the answer in synthetic division?

Back

The answer is written as a polynomial of one degree less than the original polynomial.