Polynomial Division: Long and Synthetic

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers.

Front

What is the difference between long division and synthetic division?

Back

Long division is a method that can be used for any polynomial division, while synthetic division is a shortcut method that can only be used when dividing by a linear factor.

Front

What is the first step in polynomial long division?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

What is a remainder in polynomial division?

Back

The remainder is what is left over after dividing one polynomial by another, and it can be expressed as a polynomial of lower degree than the divisor.

Front

How do you write the result of polynomial division?

Back

The result is written as the quotient plus the remainder divided by the divisor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear polynomial of the form (x - c).

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

A zero placeholder is used to maintain the correct degree of the polynomial when a term is missing.

Front

How do you determine the number to use in the left-hand box for synthetic division?

Back

The number in the left-hand box is the value of c from the divisor (x - c).

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.