Flashcard 4.3: 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

What is the first step in synthetic division?

Back

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

Front

In synthetic division, what do you place in the left-hand box?

Back

The zero of the divisor, which is the value of c.

Front

How do you set up the coefficients for synthetic division?

Back

List the coefficients of the polynomial in descending order of degree, filling in zeros for any missing degrees.

Front

What is the result of synthetic division?

Back

The result is a polynomial of one degree less than the original polynomial, along with a remainder.

Front

What does the remainder represent in synthetic division?

Back

The remainder represents the value of the original polynomial evaluated at the zero of the divisor.

Front

How do you write the final answer after synthetic division?

Back

Combine the quotient polynomial with the remainder, expressed as R/(x - c).

Front

What is a polynomial?

Back

An expression consisting of variables raised to non-negative integer powers and coefficients.

Front

What is a binomial?

Back

A polynomial with exactly two terms.

Front

What is the degree of a polynomial?

Back

The highest power of the variable in the polynomial.