Polynomial Division

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 the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

How do you perform polynomial long division?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract the result from the dividend. 4. Repeat the process with the new polynomial.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving 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).

Front

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

Back

The leading coefficient determines the end behavior of the polynomial and is crucial in the division process.

Front

What does it mean if a polynomial has a remainder of zero?

Back

If a polynomial has a remainder of zero when divided by a binomial, it means that the binomial is a factor of the polynomial.

Front

How do you find the degree of a polynomial?

Back

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

Front

What is the relationship between roots and factors of a polynomial?

Back

If r is a root of the polynomial f(x), then (x - r) is a factor of f(x).

Front

What is the purpose of adding zero terms in polynomial division?

Back

Adding zero terms helps maintain the correct degree of the polynomial during division, ensuring that all terms are accounted for.