Questions tagged [factoring]
For questions about finding factors of e.g. integers or polynomials
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Let f be a polynomial in $Q[x]$ with integer coefficients and $g = a_n^{n-1}f(a_{n-1}^{-1}X)$ where $f(x)=a_nx^n+a_{n-1}x^{n-1}+\ldots a_1x + a_0$
I apologize if it is elementary, but here goes.
Let $f$ be a polynomial in $Q[x]$ with integer coefficients define $g = a_n^{n-1}f(a_{n-1}^{-1}X)$ where $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots a_1x + ...
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ACT practice test, aren't both $3$ and $12$ viable answers?
The question
For which of the following values of $c$ will there be two distinct real solutions to the equation $5x^2+16x+c=0$?
and the possible answers are:$\quad$
$\text{F}.\space3\\
\text{G}.\...
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Is there a generalization of factoring that can be extended to the Real numbers?
I simply mean that factoring integers is well understood, but factoring an irrational or any real number does not seem to make sense, especially taking into account that a large integer many ...
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Algorithms for factorization of symbolic multivariate polynomials [duplicate]
I've been trying (but utterly failed) to find literature on how CAS implement factorization of symbolic polynomials. Everything I find relentlessly points back to stuff about rings and polynomials ...
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Factoring $N = pq$ for primes $p,q$ knowing $q\bmod (p-1)$ [closed]
Let $N=pq$ where $p$ and $q$ are both prime numbers.
If we know the value $k = (q \bmod (p−1))\, $ can that help us to factor $N$?
For example $N= 899=29\times 31$ and $\,k = 31 \bmod 28 = 3$.
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Factoring bivariate quadratic polynomials.
I want to know if there is any simple method for factoring quadratic polynomials with two variables. Can anyone recommend me a good book from where I can learn about this topic?
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Methods for factoring multivariate polynomials. [duplicate]
Can anyone give me some ways to factorized a polynomial in the form of ax^2+2hxy+by^2+2gx+2fy+c ? Any reference book would also be appreciated.
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Why do $n^4+4$ and $(n+2)^4+4$ have a largish common prime factor? [duplicate]
It seems that $n^4+4$ and $(n+2)^4+4$ always have a prime factor other than $2$ or $5$. For example: $94^4+4$ and $96^4+4$ are both divisible by $4513$; $15^4+4$ and $17^4+4$ are both divisible by 257....
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Properties of Nth roots and fractional powers
Context: I'm programming an arbitrary precision math library and created some weird algorithms to calculate a number raised to non-integer powers due to optimizations.
From my understanding, raising ...
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Irreducible elements, prime elements, prime ideals, and maximal ideals [duplicate]
I'm trying to get the four concepts listed in the title straight in my mind and elucidate the relationship between them. Could someone check the following statements and let me know if they are all ...
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Can I use the slope of $\sqrt{N}$ to factor semiprimes? I get an equivalence if I try. How can I use related rates?
I need to make two definitions before I get to my question, which is at the bottom.
Domain: is the X-axis (variable)
Range: is the Y-axis
$$f(Domain) = Range$$
I think semiprimes can be factored by ...
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What is range of $P$ values and range of $Q$ values for any given semiprime $N$?
Given $PQ = N$ where $P<Q$ and both $P$ and $Q$ are odd. I determined that the range of values for $P$ is: $\frac{\sqrt{N}}{2} < P \le \sqrt{N}$ and the range of values for $Q$ is: $\sqrt{N} <...
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Using Rational Root Theorem on big numbers for polynomials
One of the things I have tried finding answers to, but have always bothered me is about Rational Root Theorem when being applied to problems such as factoring of polynomials such as:
$k^3 + 6k^2 -...
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Division property of outer product? [duplicate]
$A = \{a_1,\cdots,a_m\}$ is a multiset consisting of $m$ non-negative real numbers, with at least one element $a_k > 0$.
$B = \{b_1,\cdots,b_n\}$ and $C = \{c_1,\cdots,c_n\}$ are two multisets each ...
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Is integral regular ring a UFD?
Let $A$ be a commutative ring such that it is regular and integral. It is known to all that for any prime ideal $\mathfrak{p}$ of $A$, $A_{\mathfrak{p}}$ is a UFD. My question is, whether $A$ itself ...
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