# Questions tagged [factorization]

Questions on factoring various types of mathematical expressions, with the use of Factor, FactorInteger, FactorSquareFree and related commands.

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### How to speed up Factor?

Try the following code ...
• 571
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### How to divide a known root out of a polynomial?

Consider this simple 5th order polynomial: pol=x^5+x^4+1 Factor[pol] (* (1+x+x^2)(1-x+x^3) *) root=FindInstance[pol==0, x] (* -1/2 -I/2 Sqrt[3] *) ...
382 views

### How to get the analytical form of a solution to an algebraic equation?

The real analytical solution of the algebraic equation $x^5 + 10 x^3 + 20 x == 4$ is $x=-2^{2/5} + 2^{3/5}$, how to get it with Mathematica? I've tried with ...
• 411
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### How to Factor Out Polynomial Terms which Have Same Coefficient Differing Only by Sign

I'm new to the Mathematica StackExchange. I am trying to simplify a polynomial in Mathematica. In the following, I only show a part of the polynomial Here I want to combine terms with the same ...
56 views

### How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
315 views

### Better Factorization

It seems Mathematica likes to factor some things in less than optimal ways. For example, for the oscillating exponential function (F) below, is there any way to force it to reduce both the number of ...
• 1,187
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### How to factorize $x+y$ in this kind of example?

Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
• 553
42 views

### How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed]

I what to factor a polynomial with complicated symbolic coefficients Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2] In ...
1 vote
93 views

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### Extract subscript of variable in product

My input is a product of the variable x with index: x[1]^2 x[5] x[7] How do I extract the indices of the above product to get ...
• 13
173 views

### How to prime factorise rational numbers [closed]

I'm aware of the built-in FactorInteger command for finding the prime factorisation of integers. Is there a convenient way of determining the same thing for a rational number, where the prime ...
• 1,043
136 views

### Factorizing large numbers [closed]

I am trying to factorize large prime numbers with the code bellow. The code works properly for values like 1927 and 69527 (results), but gives no result for larger values like 655051. The code goes as ...
1 vote
138 views

### How can I test if the sum of two divisors of a number add up to a perfect square? [closed]

Let's say I have a number $n$ and I want to find the divisors of $n$, I can do that using Divisors[n]. That will generate a list ...
• 2,021
104 views

### Return the factors of a partially-factored polynomial, without factoring

Suppose I have an integer polynomial f that is in a factored form, say f = (1 + x) * (2 + x + x^3) * (2 + x^5). I want a ...
163 views

### Check if polynomial is in factored form, without factoring

I have a large list list of integer polynomials, all of which are the output of Factor. So my list looks something like this: <...
156 views

### About Fermat's Integer Factoring algorithm

An implementation of Fermat's algorithm that is a slight improvement on code in this book is here. ...
• 7,144
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### Speeding up FactorInteger for product of two primes

I have a large integer $N$ of size about 10^150. I know that $N$ is a product of two primes $p$ and $q$. I also know that both $p$ and $q$ are of roughly equal size, so one of them is not, for example,...
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1 vote
187 views

### How to factorize $f(x,y)$ into $f_1(x)f_2(y)$? [duplicate]

Suppose we have a real function $f:\mathbb R^2 \rightarrow \mathbb R$ and we would like to know if this function factorizes into $f(x,y)=f_1(x)f_2(y)$ for some real functions $f_1,f_2$. Is there an ...
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How can I factor terms with variable coefficients? For example for the expression: $x^2 + a$ I know that I can factor this to: $(x+i\sqrt{a})(x -i\sqrt{a})$ How do I do this in mathematica? I would'...