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Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
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Rewrite a real polynomial in real (but only linear and quadratic) factors

According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real zeros....
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Removing 1 from FactorInteger

I am trying to remove the factor of 1 out of FactorInteger, so that I can search though numbers with common factors easier. Here is what I have already: For[n = 0, n < 10, n++; b = FactorInteger[...
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Selecting divisors of a large number that meet some criteria using the factors list

I have a list that represents a factorization of a number: its format is identical to the output of FactorInteger. I need to select the divisors that meet some ...
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Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
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How to write an expression in the desired form?

I have the following code: ...
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Getting mathematica to factor out constants and apply euler's identity to a table

I'm doing some quantum mechanics homework that I'm going to eventually generalize to higher spin states, so the solutions are going to need to be decently independent of the dimensions of the table ...
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Factoring rationals from equation based on digit complexity?

Consider an equation of the following type: ( poly = (3 x)/35 + (6 y)/7 ) == 0 If we apply the command Factor to this ...
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How to replace $-x^{}\,y^*-y^{}\,x^*$ by $-(x^{}\,y^*+y^{}\,x^*)$?

Up to now, I have tried some codes like the following: ...
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decomposing an expression into absolutely positive terms

I have a big ugly expression which, for unimportant (here) reasons, must be greater than or equal to zero. It is formed from terms which themselves are greater than or equal to zero. As such it ...
351 views

Factoring out a common term

Very simple question, but I can't find a simple answer here or in the documentation. I have an expression: qq = a x + b x^2 + c x^3 and wish to factor out a ...
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Factor terms by kets

I have an expression that contains several kets with numerical factors. I would like to retrieve the individual kets and store each individually as a list element. The expression is as follows: <...
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Is Factor reliable to find factorization? [closed]

I have two polynomials given by: ...
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Factorize and find the null space of a polynomial in several variables [duplicate]

I've been asked to factor the following polynomial: poly = 6 x^3 + x^2 y - 11 xy^2 - 6 y^3 - 5 x^2 z + 11 xyz + 11 y^2 z - 2 xz^2 - 6 yz^2 + z^3 And to solve for z so that poly = 0 Can anyone help ...
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Explicitly find a guaranteed factorization of large expression?

Consider the large expression LE defined in this file (involving only linearly independent functions), or in this file (linear interdependence present but slightly ...
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Relative factorisation with scalar quantities

I'd like to find a natural way to tell mathematica that a given unknown in a polynomial should be treated as a number, unlike the other variables. Typically I'd like to sum two polynomials in several ...
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can I expand non-integer powers

How can I help Mma to recognize that w can be factored out of (a w)^a (w - a w)^(1 - a). Assumptions: w>0 and 1>a>0.
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Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
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Factoring the imaginary unit

Suppose you have this: Collect[2 u + I + 2 + I,I] It gives the same. Is it possible to factor I in elegant way (not manually)...
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Tell Mathematica to factor something specific

Is there a way to tell Mathematica to factor $$\frac{1}{1-x^2}$$ from a large expression? For instance if the expression is A_1+A_2+A_3 and I want to factor ...
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Factoring large integers with the Pollard p-1 method

I am trying to use the Pollard $p-1$ method to find the factors of a large integer. Here is the problem: An RSA-type cipher is based on the integer $n = 140016480344628383$ and exponent $2345671$...
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Factor out certain terms using Modulus but Mathematica requires that the modulus be an integer [closed]

Mathematica demands that the modulus be an integer. How do I work my way around this?
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Transforming functions

I am not familiar with Mathematica but have the following question: I am trying to write Mathematica code that transforms $x^a+y^a$ to $(x+y)^a$ for any $x$ and $y$ and integer $a$. I also need to ...
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Splitting a polynomial into sum of factors, not necessarily linear

How can I split a given polynomial as sum of factors in Mathematica? For example, let's say I have this polynomial: $2\cdot x^2+7\cdot x+2$. I would like the output to be $(x+1)(x+2)+x(x+4)$. Is ...
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Factoring problem

Keep factoring and concatenating starting with 2 until we get a prime, i.e. 2 = 2 ; 22=2.11 ; 22211=7.19.167 ; 22211719167=..... and so on (the prime factors are arranged from smaller to larger and ...
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Factor bivariate polynomial over the complex numbers

This is very much like Factoring polynomials to factors involving complex coefficients except that I'm concerned about bivariate polynomials, not univariate polynomials. Take for example the ...
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Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
460 views

Specific factoring of fourth degree polynomial

I have a pretty unspecific question about a really specific thing -- How would one use Mathematica to find values for an integer, m, such that this polynomial ...
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I was hoping to find an elegant solution to this riddle, using only a line or two of Mathematica: Santa Claus was telling one of his elves: "If I multiply the age of three of my reindeer, I get ...
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Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
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How to factorise a variable out of an indefinite sum?

(I should start by saying I'm a total beginner with Mathematica, so if the answer needs code I'll need it spelled out quite clearly, the learning curve for this is proving steep!) Basically what I am ...
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factorization of integer into two parts with specific prime factors

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals. For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
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Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or <...
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Collecting terms in an expression [duplicate]

I have an expression: ...
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How do I create a list of 25 random quadratic equations in the form ax^2+bx+c?

My teacher suggests using the RandomInteger command along with the Factor command, but I cannot figure out the syntax. A, b, and c need to be non zero integers between -10 and 10.