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Ohio Open Ed Collaborative
Mathematics, Tmm0022
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Polynomial Division - The Factor and Remainder Theorems

Factor and Remainder Theorems, Long Division and Synthetic Division

It would be helpful to review factoring principles for binomials and trinomials.

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