Polynomial Division

Front

What is polynomial division?

Back

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

Front

What is the result of dividing a polynomial by a linear factor?

Back

The result is a polynomial of one degree lower than the original polynomial, plus a remainder.

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

When should you use long division instead of synthetic division?

Back

Use long division when dividing by a polynomial of degree greater than 1 or when the divisor is not in the form (x - c).

Front

What is the remainder theorem?

Back

The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

Front

What is the factor theorem?

Back

The factor theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you write the answer to a polynomial division problem?

Back

The answer should be written in the form: quotient + remainder/divisor.

Front

What is the first step in polynomial long division?

Back

Divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient.

Front

What is a zero placeholder in synthetic division?

Back

A zero placeholder is used in synthetic division to represent missing terms in the polynomial, ensuring that all degrees are accounted for.

Front

What is the significance of the leading coefficient in polynomial division?

Back

The leading coefficient affects the degree and the behavior of the polynomial as x approaches infinity or negative infinity.