Factor Cubic Equations

Factor Cubic Equations

Factor Theorem (FT)

Corollary

For all fields , all polynomials , and all , the linear polynomial is a factor of the polynomial if and only if , meaning is a root of the polynomial

That is, is a factor of if and only if .

Examples

Example

Factor

solution let

  1. Find a factor of the equation
    Find such that and




    is a factor of

  2. Using Polynomial Long Division, divide the the equation by the found factor

  3. Factor
    Factor the trinomial

Example

Factor

solution let

  1. Find a factor for
    Factors of constant term:
    Factors of coefficient:
    Factors of :





    is a factor of

  2. Using Polynomial Long Division, divide the equation by the found factor

  3. Factor