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how to find factors for a third degree equation other than horners method

6 years ago


Answers : (2)


Dear viswateja,

General Method for Cubic & higher degree polynomial is Synthetic Division.
Factorise the polynomial by trail & error method which reduces into Quadratic polynomial (II nd degree polynomial ) then,as usual procedure (U may know it )
Another quicker method is,

Descartes’ Rule of Signs:

  • The number of positive roots of p(x)=0 is either equal to the number of variations in sign of p(x), or less than that by an even number.

  • The number of negative roots of p(x)=0 is either equal to the number of variations in sign of p(−x), or less than that by an even number.

If sum of coeffcients of odd degree = sum of coeffcients of even degree ( including constant term ), then (x+1) is a factor and hence (-1) is a root.
If sum of coeffcients of odd degree & even degree = 0 , then (x-1) is a factor and hence 1 is a root.
If the above said doesnt work then go for other numbers both negative as well as positive.


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6 years ago

Dear student,

Follow this procedure step by step:

  1. If solving an equation, put it in standard form with 0 on one side and simplify

  2. Know how many roots to expect.

  3. If you’re down to a linear or quadratic equation (degree 1 or 2), solve by inspection or the quadratic formula.  
    Then go to step 7.

  4. Find one rational factor or root. This is the hard part, but there are lots of techniques to help you.
    If you can find a factor or root, continue with step 5 below; if you can’t, go to step 6.

  5. Divide by your factor. This leaves you with a new reduced polynomial whose degree is 1 less.  
    For the rest of the problem, you’ll work with the reduced polynomial and not the original. Continue at step 3.

  6. If you can’t find a factor or root, turn to numerical methods. 
    Then go to step 7.

  7. If this was an equation to solve, write down the roots. If it was a polynomial to factor, write it in factored form, including any constant factors you took out in step 1.

We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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Sagar Singh

B.Tech IIT Delhi

6 years ago

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