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

learn more… | top users | synonyms

1
vote
1answer
25 views

Deflating (factoring) a 6th degree polynomial

What is the procedure to factor a 6th degree polynomial of a complex variable? $$P(z)=1+x^2+x^3+x^4+x^5+x^6$$ I do have the correct answer but no idea how to get to it. The answer is: ...
0
votes
2answers
47 views

Direct Proof even and odd

In trying to show that $n$ is even, is my final solution correct? First: If $n$ is even then $n^3+n$ is even. Since $n$ is even, then: $$n=2\cdot s$$ $$n^3+n = (2\cdot s)\cdot (2\cdot s)\cdot (2\cdot ...
0
votes
3answers
52 views

tough factorisation problem

How would you factorise this equation given that $x=7$ is a root of this equation $$x^3 - 67x + 126 = 0.$$ Any help would be thoroughly appreciated.
1
vote
1answer
26 views

Polynomial Factoring over a finite field

Ok, so I'm trying to figure out how to factor polynomials over a finite field. My polynomial is x^5 + x^2 + x + 1 and I have to factor over GF(2) I know the answer is (x+1)^2 * (x^3 + x + 1), because ...
0
votes
0answers
35 views

Solving equation in maxima not placing variable on one side

I'm trying to solve an equation but the variable ($\varphi$ PHI) will not factor out to one side. Is there any other way to do this? I'm using maxima version 5.32.1 Here's the equation in latex as ...
6
votes
3answers
124 views

Polynomial factorisation - absolute value of coefficients

This question takes the factorisation of a polynomial $p(x)=q(x)r(x)$, where $p$ (and for my purpose here $q$ and $r$) have integer coefficients and asks if the maximum absolute value of the ...
1
vote
2answers
46 views

How to find an alternate form of this polynomial (factorize?)

I am trying to find the limit of the function $$\lim_{t \to 1} {{t^3-2t+1}\over{t^3+t^2-2}}$$ And it obviously evaluates to ${0\over0}$ so at first glance it is indetermined. But I have these two ...
1
vote
3answers
200 views

Factoring the Polynomial $x^4-2x^2+1$

Okay, I am practicing factoring for an upcoming assignment and I know that this is basic algebra, but I forgot how to attack this polynomial. Every method that I have used so far from simply guessing ...
0
votes
0answers
24 views

Integer Factorization

if $x \not \equiv \pm y$ (mod $n$) and $x^2 \equiv y^2$ (mod $n$), then $\gcd(x \pm y, n)$ are factors of $n$. Proof: $x^2 \equiv y^2$ (mod $n$) $\Rightarrow n$ is a factor of $(x-y)(x+y)$. Note ...
1
vote
0answers
42 views

Binary Polynomial Factoring

I just need confirmation that I've done my math right. If $a(x) = x^4 + x^3 + x + 1$ and $b(x) = x^2 + x + 1$ are binary polynomials, find binary polynomials s(x) and r(x) such that $x^4 + x^3 + x + ...
2
votes
4answers
79 views

Solving $y^2 - yx - y + x = 0$ for $y$?

I solved this equation for $y$ by inspection and confirmed it with Wolfram Alpha - $y^2 - yx - y + x = 0$ I got the values $y = 1$ and $y = x$ However I was wondering is there a formal method for ...
0
votes
2answers
27 views

Solving a polynomial equation by factoring

The polynomial f(x) is defined by $$f(x) = 12x^3+25x^2 -4x -12$$ (i) Show that f(-2) = 0 and factorise f(x) completely. Which i did and got $(x+2)(3x-2)(4x+3)$ (ii) Given that $$12 * 27^y + 25 * ...
0
votes
1answer
19 views

Factoring binary polynomials

I need to factor two binary polynomials and present each as a product of powers of irreducible polynomials. a) x⁴ + 1 I have figured it out this far: x⁴ = (x²)² and 1 = 1² So I have something in ...
0
votes
1answer
20 views

how to find the interval at which a derivative function is increasing

Alright, so here's the deal. I need to find the interval of this derivative function: f(x)= −5x2+12x−7 So far, I've gotten that the derivative is this: ...
-1
votes
1answer
33 views

Factoring/Expansion explantion

Sorry if I call something by the wrong name since I didnt learn math in english. ok so for example this: (a+b)(a-b) if you break it down to the second "()" you will end up with this: a+-b could ...
4
votes
3answers
69 views

How to factor $x + 1 - 2 \sqrt x$?

My teacher said the answer is $(\sqrt x -1)^2$, but I want to know how he figured it out. I know it's a trick I learned years ago, but I can't remember how to do this.
0
votes
0answers
22 views

Factoring big numbers into primes

I can't find a good tutorial anywhere on how to factor big numbers into primes, so I was wondering if someone could explain the process. I need to do this for my cryptology class.
2
votes
1answer
21 views

Evaluating cubic roots of a quadratic

If $\alpha$ and $\beta$ are the roots of the quadratic equation $2x^2 + 4x -5 = 0$, evaluate $\alpha^3 + \beta^3$.. I know that $$\alpha + \beta = \frac{-b}{a}$$ and $$\alpha \beta = ...
-1
votes
2answers
58 views

Fully factorise $x^3-x^2-14x+24$ into linear factors

$$f(x)=x^3-x^2-14x+24$$ I've tried grouping the terms, but it just doesn't work out for me. Any help is appreciated.
1
vote
2answers
35 views

Factoring somewhat complex polynomial

Can this be factored? $$m^2(a-1) + 2m(a-1) -1$$ I have not been able to find any roots that will work when multiplied out. Does anyone see any options?
0
votes
1answer
31 views

yacas factorize polynoms

I want factorize polynoms with yacas but I can do it only with univarial. E.g. I want $x^2-y^2$ factorize to $(x-y)(x+y)$. How can I do it? Or if anybody has any suggestion to another simple, free ...
1
vote
2answers
30 views

Factor the Quadratic

-16t^2+32t+20=0. How are you supposed to find -5 and positive 1 to put in the parenthesis? -4(2t-5)(2t+1)?
2
votes
3answers
79 views

Finding all natural $n$ such that $2^n+2^{2n} +2^{3n}$ has only $2$ prime factors.

Find all natural $n$ such that $2^n+2^{2n} +2^{3n}$ has only $2$ prime factors. I've tried checking the first 6-7 $n$'s on wolframalpha, but I don't see any patterns for even nor odd $n$'s. At first ...
0
votes
2answers
32 views

Completely factor a polynomial using the rational root theorem and synthetic division

I am currently seriously confused. My problem, as stated above, is about completely factoring a polynomial. My question is, once you get your possible factors, how do you then simplify it down? Ill ...
0
votes
1answer
29 views

Regarding +/- fractions: what are some mental tests you can apply to uncommon fraction denominators?

When adding and subtracting fractions: what if there is no uncommon factor (for example 4=2,2 and 6=2,3). Does that always mean to use the LCM? What if the LCM is too big or time consuming to ...
1
vote
3answers
67 views

Factorize $6x^2 -5x -14 = 0$

I'm throwing a bit of a blank on the best way to factor this : $$6x^2 -5x -14 = 0$$ I know that I could multiply $6$ by $14$ and then find a pair of factors that add to $-5$ (b), but this feels a ...
0
votes
1answer
23 views

Prove that a polynomial an irreducible g has no multiple root in C

I was looking at a question from Artin from Algebra which says that an irreducible polynomial g in F[x] where F is subfield of $\mathbb{C}$. So as per the proofs I have seen so far says as - ...
1
vote
1answer
28 views

Simplifying square roots?

How would I simplify $\sqrt{\frac{800}{3}}$ preferably by a factor tree? I know it simplifies into $\frac{20\sqrt{6}}{3}$. I just don't know the steps to get there. Help please?
1
vote
2answers
66 views

Find the limit of a Riemann Sum

The function is $f(x) = 1-x^2$. I'm stuck as I can't factor the expression in the last line to find the limit.
0
votes
0answers
26 views

How to factor $(1-(i^2/n)(1/n)$ to isolate $i^2$ and form a sigma identity?

given sigma from $i=1$ to $n$ of $(1-(i^2/n)^2)(1/n))$ how would you factor this function to isolate $i^2$ and get $[n(n+1)(2n+1)]/6$ ? update... I got until the limit as n approaches infinity (1/n) ...
1
vote
2answers
38 views

Notation: is a factor of

How can one write $x$ is a factor of $y$ (as a constraint)? I am also not sure what else to add to meet the question quality requirements.
0
votes
0answers
68 views

Find factors of $0.08x^3 - 3.84x^2 + 42.66x - 137.7625$ using the Cubic Formula.

I have been going over this page as of late learning how to solve cubic formulas through depressing the equation, and solving for 'X'. Though, so far through numerous attempts, every single root I ...
1
vote
3answers
62 views

How do I factor $\ t^4-2 \ $?

This binomial is part of a bigger problem that I need to solve, however, I am little stuck on how to factor it. $(t-1)(t-1)(t+1)$ does not work.
0
votes
1answer
40 views

Factor Theorem given two factors

The function $f(x)= ax^3-x^2+bx-24$ has three factors. Two of these factors are $x-2$ and $x+4$. Determine the values of a and b and then solve for $f(x)$. Please give an algebraic solution.
2
votes
2answers
62 views

Number of Relatively Prime Factors

Given a number $n$, in how many ways can you choose two factors that are relatively prime to each other (that is, their greatest common divisor is 1)? Also, am I going in the correct direction by ...
0
votes
2answers
21 views

Can a logistic function(x+y) be approximately factored into $f_1(x)$ and $f_2(x)$?

I need to somehow factor the logistic function $$\frac{1}{1+e^{-(\theta-\beta)}}$$ into $f_1(\theta)$$f_2(\beta)$ approximately... namely $\frac{1}{1+e^{-(\theta-\beta)}} \approx ...
1
vote
4answers
113 views

For how many $n$, $x^6+n$ factors?

$\textbf{Question}.$ i) For how many integers $n$ with |$n$|$<500$, can the polynomial $p_n(x)=x^6+n$ be written as a product of two non-constant polynomials with integer coefficients? ii) How ...
4
votes
2answers
326 views

Definition of factor - Is n a factor of n?

Is there a universally agreed upon definition of what a factor of a number is? Is $n$ a factor of $n$? Is $1$ a factor of $n$? EDIT x 2: Integers Natural Numbers
0
votes
1answer
64 views

Factorizing Cubic Equations.

Factorization of Cubic Equations has always obstructed my way to the solution to a problem. Is there any simple technique to factorize them?
1
vote
2answers
34 views

Factoring Polynomial with Four Terms

To begin, I have the following equation: $f(x)=2x^2-5x$. Now I need to find the roots of $f(f(x))$. I also know that $f(x(x))$ simplifies to $8x^4-40x^3+40x^2+25x$. It's very obvious to me that a $x$ ...
0
votes
3answers
71 views

Rearranging the polynomial $x^3-23x^2+142x-120$ prior to factoring it

In the example 15: They are saying that, $$x^3-23x^2+142x-120 = x^3-x^2-22x^2+22x+120x-120$$ From where did $22x^2$ and $22x$ come and also $120x$. Please help me clear my confusion.
2
votes
4answers
25 views

Is $5^2x^3-x^5 = x^3(x-5)(x+5)$ or $-x^3(5-x)(5+x)$

Geogebra's Factor function says that $5^2x^3-x^5$ is $-x^3(x-5)(x+5)$ but from what I do, it is positive, $x^3(5+x)(5-x)$ Note the x isnt in the same position Am I wrong?
3
votes
3answers
61 views

How to factor $(x^5+1) (x^5-1) $

I have this: $ (x^5+1) (x^5-1) $ And I don't know how to continue factor. Geogebra's Factor says: $(x+1)(x-1)(x^4-x^3+x^2-x+1)(x^4+x^3+x^2+x+1)$
0
votes
1answer
30 views

factorization to determine convergence/divergence

Let: $$f(n) = n/(n^4+1)$$ if we factor f to: $$ n/[n^3(n+1/n^3)] $$ Given that this is equivalent, we perform distribution: $$1/[n^2(n+(1/n^3)]$$ We now have: $$ 1/(n^3+1/n) $$ So: $ 1/n ...
0
votes
2answers
53 views

finding solutions by factoring

How would you find the integer solutions to $a^2-b^2=16$? I know that the factors of $16$ are $8*2,$ $4*4,$ and $16*1.$ How would I use this? I know that $a^2-b^2=(a+b)(a-b)=16,$ but how would you ...
0
votes
0answers
24 views

How to decompose N into A and B so that A and B are close to each other.

I would like to decompose $N$ into $A$ and $B$ so that $A$ and $B$ are close to each other. Even I would allow some small error. Se I would like to have: $$N = A*B + \epsilon_N$$ where $$\epsilon_N ...
2
votes
1answer
29 views

factor $y'$ as $y' = f(x)g(y)$

I have a task where I have to write following differential equation as $y' = f(x)g(y)$ but I see no way you could factor it into two functions each only depending on $x$ respectively $y$: $$y' = ...
0
votes
0answers
62 views

Positive integers of sum and products

Find all pairs of positive integers $m$ and $n$ where $m<n$ such that the sum of $m$ and $n$ added to the product of $m$ and $n$ is equal to $2014$ I just thought about this question and ...
0
votes
2answers
66 views

Pair of positive integers in product sums

I am still not sure on this answer. I would like someone to help me see the solution to his question. I was working on it for a while and it is the only question that I looked at that I can not ...
0
votes
1answer
71 views

Largest prime factor of a number

In Project Euler problem 3, where we have to find the largest prime factor of a number, one of the solution i came across is ...