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

How do you set up Synthetic Division?

Back

Write the coefficients of the polynomial in a row and place the zero of the divisor 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 brought down coefficient by the zero of the divisor and add it to the next coefficient.

Front

What does the final row of numbers represent in Synthetic Division?

Back

The coefficients of the quotient polynomial and the remainder.

Front

How do you interpret the result of Synthetic Division?

Back

The result gives the quotient polynomial and the remainder, which can be expressed as: quotient + remainder/(divisor).

Front

What is the remainder theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How can you check your work after performing Synthetic Division?

Back

Multiply the quotient by the divisor and add the remainder; the result should equal the original polynomial.

Front

What is the significance of the degree of the polynomial in Synthetic Division?

Back

The degree of the quotient will be one less than the degree of the original polynomial.