Vocabulary
Polynomial Long Division- A method used to divide polynomials similar to the way you divide numbers.
Synthetic Division- A method used to divide a polynomial by a divisor of the form x - k.
Synthetic Division- A method used to divide a polynomial by a divisor of the form x - k.
Essential Information
When a polynomial, f(x), is divided by a divisor, d(x), a quotient polynomial, q(x), is formed and a remainder polynomial r(x).
The degree of the remainder must be less than the degree of the divisor. One way to divide polynomials is through polynomial long division.
Synthetic Division
Remainder Theorem
If a polynomial f(x) is divided by x-k, then the remainder is r = f(k).
If a polynomial f(x) is divided by x-k, then the remainder is r = f(k).
Factor Theorem
If the remainder is 0 when a polynomial f(x) is divided by x-k, Then
If the remainder is 0 when a polynomial f(x) is divided by x-k, Then