# Questions tagged [factoring]

For questions about finding factors of e.g. integers or polynomials

2,377 questions
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### Selecting a finite field for polynomial factorization

This is a very specific question about factoring standard polynomials in the field of rationals. I have a module written which does the whole chain of square-free factoring to distinct-degree ...
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### Factoring $(x+a)(x+b)(x+c)+(b+c)(c+a)(a+b)$ and use the result to solve an equation

I managed to prove that $(x+a+b+c)$ is a factor of $$(x+a)(x+b)(x+c)+(b+c)(c+a)(a+b)$$ Then I was asked to use the result to solve $$(x+2)(x-3)(x-1)+4=0$$ I know by comparison, $a=2, b=-3, c=-1$, ...
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### How to compute gcd of two polynomials efficiently

I have two polynomials $A=x^4+x^2+1$ And $B=x^4-x^2-2x-1$ I need to compute the gcd of $A$ and $B$ but when I do the regular Euclidean way I get fractions and it gets confusing, are you somehow able ...
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### batch factoring

The table below illustrates a snapshot of results for a potential way to factor particular integers. Each C value denotes a particular "curve" of the method. The index value logged to the respective ...
0answers
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### Matrix Equation AB = C with constraints, where both A and B are unknown.

As the title reads, I have the matrix equation: $$AB = C$$ With the constraint that all elements in B are greater than $0$ and less than $1$, and the last element of each row is $1$. A and B can be ...
1answer
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### Find the smallest integer n > 1 such that the product of the factors of n is $n^{15}$ [on hold]

Find the smallest integer n > 1 such that the product of the factors of n is $n^{15}$
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1answer
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### Recognising a Factoring Pattern

I am trying to identify a pattern in the following set of equations; $$N_0=y$$ $$N_1=y^2+z$$ $$N_2=y^3+2yz$$ $$N_3=y^4+3y^2z+z^2$$ $$N_4=y^5+4y^3z+3yz^2$$ $$N_5=y^6+5y^4z+6y^2 z^2+z^3$$ Essentially, ...
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### Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$

Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$ By factor theorem we know that $(x-a)$ is a factor of $f(x)$ if $f(a)=0$. In this case, $f(x)=x^n -nx +n-1 \implies f(1)=0$ Hence we conclude that ...
5answers
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### How to factorized this 4th degree polynomial?

I need your help to this polynomial's factorization. Factorize this polynomials which doesn't have roots in Q. $\ f(x) = x^4 +2x^3-8x^2-6x-1$ P.S.) Are there any generalized method finidng 4th ...
0answers
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