Polynomial Division Review

Front

What is polynomial division?

Back

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

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing than long division.

Front

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

Back

A zero placeholder is used in synthetic division to maintain the correct degree of the polynomial when a term is missing, ensuring accurate calculations.

Front

How do you determine the remainder in polynomial division?

Back

The remainder can be found by evaluating the polynomial at the root of the divisor. For example, if dividing by (x - c), substitute c into the polynomial.

Front

What is the result of dividing (x^4 + 3x^2 - 4x - 2) by (x - 2)?

Back

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

Front

What is the significance of the degree of a polynomial in division?

Back

The degree of a polynomial indicates the highest power of the variable. In division, the degree of the dividend must be greater than or equal to the degree of the divisor.

Front

What does it mean if a polynomial division problem is incorrect?

Back

It means that either the calculations were performed incorrectly, or the polynomial was not set up properly for division.

Front

What is the correct way to express the answer to a polynomial division problem?

Back

The answer should be expressed as a polynomial plus a remainder, or as a quotient with a remainder term.

Front

What is the first step in synthetic division?

Back

The first step is to write down the coefficients of the polynomial in descending order of degree.

Front

How do you handle missing terms in polynomial division?

Back

You represent missing terms with a coefficient of zero to maintain the correct structure of the polynomial.