How to Identify Prime Polynomials in Algebra

Factoring polynomials is one of the building blocks of algebra.
••• Jupiterimages/Photos.com/Getty Images

An algebra student gets stuck when exhausting all factoring steps, can't find the answer, but forgets to consider a prime polynomial. These polynomials, like prime numbers, are in lowest common terms and you cannot factor them further. Here is how you recognize such an equation.

    Go through all the usual steps for factoring. First check for common monomial factors.

    Try the special formulas for factoring perfect squares, and then use the first formula for factoring a second-degree polynomial, x^2 + Bx + C, and see if it works.

    Apply the other special formula for factoring a second-degree polynomial of the form: Ax^2 + Bx + C.

    Exhaust all normal steps of factoring before deciding that you have a prime polynomial on your hands.

    Use the following as an example to help you learn to identify any prime polynomials you may come across: x^2 + 2x + 8. Set up a pair of two parentheses with the x's in place: (x + )(x + )

    Look for two numbers whose product is 8 and sum is 2. Check for the 2 and 4 when both are either plus or both are minus, for 8. Try 1 and 8 with both plus or minus for the positive 8. None of these four sets of numbers equal 2.

    Declare the polynomial equation prime. You have looked at every possible way to factor the equation. It does not factor by a Greatest Common Factor or by special formulas. You have a prime polynomial on your hands.

Related Articles

Methods for Factoring Trinomials
How to Factor Polynomials Step-by-Step
How to Solve Double Inequalities
How to Write an Absolute-Value Equation That Has Given...
How to Solve Binomial Equations by Factoring
How to Factor Prime Trinomials
How to Factor Polynomials & Trinomials
How to Find All Real Solutions of an Equation
How to Factor Trinomials, Binomials & Polynomials
How to Write the Prime Factorization in Exponent Form
How to Solve Trinomials
Rules for Factoring
How to Factorise in Math
How to Factorise a Quadratic Expression
Tricks for Factoring Quadratic Equations
How to Find the Zeros of a Function
How to Find the Intersection of Two Linear Equations
How to Find the Sum And Difference of Cubes
How to Solve for a Variable
When Do You Flip the Inequality Sign?