Polynomials are expressions involving variables and their powers, written in descending order. To divide one polynomial by another, we use long division, writing the division statement as P(x) = (x - a)Q(x) + R, where P(x) is the dividend polynomial, (x - a) is the divisor binomial, Q(x) is the quotient polynomial, and R is the remainder. For example, to divide -4x^4 + 2x^2 - x - 3 by x - 3, we would use long division.

1. Polynomials
n n-1 n-2 2
n n-1 n-2 2 1 0
where n is a whole number
n 0

2. Review: Long Division
Ex. 425 ÷ 25 = ?
dividend divisor
How about 2748 ÷ 13?

3. 2

4. 3 2
Note: Must write the polynomial in descending order!

5. Division statement for Division by x - a
P(x) = (x - a)Q(x) + R
where P(x) is the original polynomial
(x - a) is the binomial divisor
Q(x) is the quotient polynomial
R is the remainder
Ex. Divide: -4x4 + 2x2 - x - 3 by x - 3