Linked Questions
12 questions linked to/from Factoring polynomials to factors involving complex coefficients
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How to convert $a(x-p)^2+q$ to $a(x-\alpha+i\beta)(x-\alpha-i\beta)$ for any real $a$, $p$ and $q$ [duplicate]
I want to factorize any quadratic expressions into two complex-valued linear expressions.
My effort below
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- 2,069
3
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1
answer
229
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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 ...
- 31
25
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2
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Code I get from wolfram isn't working in mathematica
I need to perform the factor as shown here
factor(s^5+32s^4+363s^3+2092s^2+5052s+4320)
https://www.wolframalpha.com/input/?i=factor(s%5E5%2B32s%5E4%2B363s%5E3%...
- 373
11
votes
3
answers
3k
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Checking if the roots of a function are real
I'm trying to determine if the roots of a function are real. How would you do that?
(In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
- 113
2
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3
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2k
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Partial fraction decomposition of $1/(e^x-1)$
This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not.
Similar is the case with one more CAS I ...
- 2,143
12
votes
1
answer
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Apart for complex roots?
Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x].
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- 13.2k
5
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1
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803
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Factoring a two variable polynomial in a special way
Let $$f=x^9-x^6+4x^5y+2x^3y^2-y^4$$
I would like to factorize $f$ into form: $$(y-F_1(x))\cdots(y-F_k(x))$$ over complex numbers. How can I do it with Mathematica?
6
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1
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Constructible numbers
Can Mathematica detect constructible numbers?
I know it has MinimalPolynomial, but for degrees higher than 4 it's not obvious whether a given polynomial yields a ...
- 1,379
1
vote
1
answer
420
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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 ...
- 125
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2
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411
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How to factor real polynomials over complex field
I'd like to factor polynomials over the complex field. For example, how do I factor x^2+1 over $\mathbb{C}$?
Factor[x^2+1] and <...
- 131
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1
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Factoring the Quadratic Polynomial $a x^2 +b x +c$
I want mathematica to factor the quadratic polynomial $a x^2 +b x +c$ into this standard form $a(x-r_1)(x-r_2)$ with $r_1=-\frac{b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}$ and $r_2=-\frac{b}{2a}-\frac{\sqrt{b^...
- 1,737
1
vote
1
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Convert complex exponential to real exponentials, sines and cosines
While taking the inverse Laplace transform of certain expressions, Mathematica yields complex exponentials. For example, using the following code:
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- 453