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Factoring trinomials

This is factoring trinomials calculator, in other words, the calculator which can factor trinomials given the three terms of the trinomial.

A trinomial is a polynomial consisting of three terms. Typical trinomials which appear in math problems have the form of quadratic trinomials

ax^2+bx+c

You are usually asked to factor these trinomials, in other words, get from trinomial to the product of two binomials. You can use the calculator below to check your results. The calculator also shows steps needed to achieve the result. General description of the steps needed to perform factoring can be found below the calculator.

PLANETCALC, Factoring trinomials

Factoring trinomials

Factored Trinomial
 

Factoring trinomials

The steps are quite simple, yet require some computations.

  1. If the first term a is negative, factor out -1 to get simpler trinomial.
  2. Look for common factor of all three terms, factor it out to get simpler trinomial. You can use calculator for The Greatest Common Factor of several numbers to do that.
  3. Find two numbers, r and s, whose sum is equal to the second term of the trinomial (r+s=b) and whose product is equal to first term multiplied by third term (rs=ac). To do that, you need to list all possible factors for the ac, and then find the factors, whose sum is b. Trinomial terms are usually simple enough for this to be done by hand, however, you can also use Factoring calculator to get all the factors.
  4. Rewrite the trinomial in the form

ax^2+bx+c=ax^2+rx+sx+c

  1. Use grouping and distributivity to finally factor the polynomial.
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