How to find factors of the 4th degree polynomial

[spalinowy]

Hello!

I have 4th degree polynomial like this:

y=x^4+18*x^3+52420*x^2+34303*x+51959400

Is it possible to present this in LV in the form like y=(a*x^2+b*x+c)(d*x^2+e*x+f) ?

I tried to use the PFE function, but I don't get the correct solution with it. I know that there is a method described by Lodovico Ferrari, but I don't know how to use it in LV

[GerdW]

Hi spalinowy,

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@spalinowy wrote:

y=x^4+18*x^3+52420*x^2+34303*x+51959400

Is it possible to present this in LV in the form like y=(a*x^2+b*x+c)(d*x^2+e*x+f) ?

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You need to solve this puzzle:

a*d = 1 (I would assume a=d=1)
a*e + b*d = 18 (= b+e, with first assumption)
a*f + b*e + c*d = 52420 (=f + b*e + c, with first assumption)
b*f + c*e = 34303
c*f = 51959400

[spalinowy]

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@GerdW wrote:

a*d = 1 (I would assume a=d=1)
a*e + b*d = 18 (= b+e, with first assumption)
a*f + b*e + c*d = 52420 (=f + b*e + c, with first assumption)
b*f + c*e = 34303
c*f = 51959400

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Is it based on some theory?
Where can I find something about it?

[GerdW]

Hi spalinowy,

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@spalinowy wrote:

Is it based on some theory?
Where can I find something about it?

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y
= (a*x² + b*x + c)*(d*x² + e*x + f)
= a*d*x²*x² + (a*e + b*d)*x³ + (a*f + b*e + c*d)*x² + (b*f + c*e)*x + c*f
= x²*x² + 18*x³ + 52420*x² + 34303*x + 51959400

Basic math…

[spalinowy]

🤝

Sometimes I have the simplest things become unclear when I slept 3 hours 😴

[Bob_Schor]

Why do you want to factor it?  LabVIEW can easily evaluate a quartic just as well as a pair of quadratics.  If you know the coefficients of the two quadratics are all integers, it shouldn't be a dfficult problem to write a LabVIEW routine to find them (best left as "an exercise for the Reader", who will probably learn something in the process).

Bob Schor

[spalinowy]

This polynomial is the denominator of transfer function. On the Bode chart there are 2 resonances, and if you divide it into two polynomials, of 2 degree will have two characteristics with single resonances.