3.1 Long Polynomial Division

Front

What is long polynomial division?

Back

Long polynomial division is a method used to divide a polynomial by another polynomial of lower degree, similar to long division with numbers.

Front

What is the first step in long polynomial division?

Back

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

Front

How do you find the quotient in long polynomial division?

Back

The quotient is found by multiplying the entire divisor by the result of the leading term division and subtracting this from the dividend.

Front

What do you do after subtracting in long polynomial division?

Back

After subtracting, bring down the next term from the dividend and repeat the process until all terms are processed.

Front

What is a remainder in polynomial division?

Back

A remainder is what is left over after dividing a polynomial when the divisor does not evenly divide the dividend.

Front

How can you express the result of polynomial division?

Back

The result can be expressed as: Quotient + \frac{Remainder}{Divisor}.

Front

What is the leading term of a polynomial?

Back

The leading term is the term in a polynomial with the highest degree.

Front

What is the degree of a polynomial?

Back

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

Front

How do you check your work after polynomial division?

Back

You can check your work by multiplying the quotient by the divisor and adding the remainder; the result should equal the original dividend.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that can be used when dividing by a linear factor.