# Factor and Remainder Theorems, Long Division and Synthetic Division

In this module we will study two important results on polynomials - the Factor Theorem and the Remainder Theorem.

The **Remainder Theorem **asserts that the value P(c) of a polynomial at a point c is the remainder on dividing the polynomial P(x) by (x - c). The quantity (x - c) divides P(x) evenly if and only if P(c) = 0, in which case, (x - c) is a **factor of P(x)**.

The **Factor Theorem** asserts that c is a zero of a polynomial if and only if (x - c) is a factor of the polynomial.

**Learning Objectives****:**

- Learn
**long division**method to divide a polynomial by another polynomial - Learn
**synthetic division**method to divide a polnomial by a linear factor (x - c) - Use the Remainder Theorem
- Use the Factor Theorem to factor a polynomial into linear and quadratic factors
- Find zeros of a polynomial