Factoring Definition and 338 Threads

Homework Statement ((a^3-b^3)/(a^2-2ab+b^2))/((2a^2+2ab+2b^2)/(9a^2-9b^2)) Not using complex number system. Not concerned with domain. Find the quotient and put it in simplest terms. Homework Equations The Attempt at a Solution Too many to transcribe. Apparently I'm missing...

Factor the expression 30(a^2+b^2+c^2+d^2)+68ab-75ac-156ad-61bc-100bd+87cd

Decompose the expression below into real factors: 1-\sin^5 x-\cos^5 x

try to determine all the positive values of k for which x^2 + 12x + k is factorable over the integers.

So I needed to factor -4x5-8x4+8x3+4x. I factored out a -4x and I am left with x4+2x3-2x2-4. The problem is I am unsure how to factor x4+2x3-2x2-4. I know how to long divide polynomials but I have not done synthetic division in over 4 years. From what I have seen on the internet it seems...

Hey, This isn't really a homework question, per se, as I am relearning some pre calculus for kicks. But I figured his would be the place to ask. For whatever reason, this very simply factoring issue has got my head spinning. I'm not exactly sure what I am doing wrong to factor this equation...

Here is the question: Here is a link to the question: Help with math question please!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement ((1/3)(y^3))+(1/y)=.5*ln((x^2)+1) Solve in terms of y Homework Equations The Attempt at a Solution I am in college differential equations, and i just can't solve in terms of y. y teacher wants that...i tried wolfram alpha, etc. How on Earth do you factor this...

Hey everyone first time poster here, I need help with some factoring of cubes. I know this might tie closely to Diophantine equations but here goes. Under what condition is the expression x^3+y^3+z^3 factorable? Where x,y,z are positive whole numbers.

Hello, I'm currently learning all about factorization techniques for a college project. I know that most of the advanced techniques are based around a congruence of squares. As part of our research we've been asked to think up an original factoring method. It doesn't matter how slow or fast...

Here is the question: Here is a link to the question: Math help: factoring? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

The purpose of this tutorial is to provide students of algebra with techniques and tips for factoring quadratic expressions. In my experience as a tutor, I have found this can be one of the more difficult and challenging topics for students. I invite anyone with any techniques of their own to...

Homework Statement see attachment Homework Equations The Attempt at a Solution I don't get the part where it says "Solving this equation for X(s), we obtain ..." Specifically jumping from 3/s(s2+3s+5) to (3/5)(1/s)-(3/5)[(s+2)/(s2+2s+5)]. How did the problem break up this...

Solve the differential equation: y(5)+12y(4)+104y(3)+408y''+564y'=0 where the (n) is the nth derivative. So it's a 5th order DE. Now I'm trying to find the roots: One of the roots is r = 0, which I obtain by factoring the equation into this form: r(r4+12r3+104r2+408r+1156) = 0...

Homework Statement I was wondering how people intuitively see how to decompose functions? For example: x^2 + 5x - 14, how do you solve that to be (x+7)(x-2) without a calculator? Do you use a specific method or do you just sit for a while trying and failing? The question is a...

I have another answer to this but I believe this one is correct. I need someone else to check it out since I have been looking at it too long. Is the bottom equality correct? \begin{alignat*}{3} \frac{\partial^2}{\partial t^2}x_1 + x_1 & = & F\cos t - 2[-A'\sin t + B'\cos t] - c[-A\sin t +...

X^4 + X^2 + (2^0.5)X + 2 - how may this expression be factorized?

I'm trying to find the derivative of: $$f(x)=(3x+1)^2(2x-3)^3 \text{ by using the product method}$$ Here is my working out so far, using product rule:$u'v+uv'$ $$\frac{d}{dx} (3x+1)^2(2x-3)^3= 2(3x+1)\cdot 3 *(2x-3)^3+(3x+1)^2\cdot3(2x-3)^2\cdot2$$ Simplified...

Homework Statement Factor x6 - y6Homework Equations a3 - b3 = (a - b)(a2 + ab + b2) a2 - b2 = (a + b)(a - b) The Attempt at a Solution I'm confused. x6 - y6 = (x2)3 - (y2)3 = (x3)2 - (y3)2 So shouldn't they all have the same factors? When I factor (x2)3 - (y2)3 = (x3)2 - (y3)2 I get...

z^4-4z^3+6z^2-4z-15 =0 How can i factor this polynomial in order to find the solutions?? I tried with the ruffini' rule. and i reached the following equation [(z+1)(-z^3-5z^2+11z-15)] =0 now how can i factor (-z^3-5z^2+11z-15) ? i tried it, but i can not solve it... :/

Alright, so I need a little brush up on my pre calc apparently! I need to determine the x-intercepts of the following function. y=x^3 + 2 I know I need to factor it... I'm just not completely sure how! Thanks!

Homework Statement Factor x + 5+ 6x^-1 Factor x^(3/2) + 2x^(1/2) - 8x^(-1/2) Homework Equations None given. The Attempt at a Solution I have tried factoring normally, it's just not working out though (for either part of the question.) I've never had to deal with this in a math...

Homework Statement Ok, just doing a re-fresher here! 2x^2 - 7x - 2 Factor it... First, let me ask you guys, when you see this, what is the FIRST thing you think of doing? The Attempt at a Solution For me... And I do not think this is correct. I would first automatically...

Lets assume you're given { 3x }^{ 2 }+8x-11 And you want to factor it. With the AC method you multiple 3 and -11 giving you -33. Then you find the factors of -33 that add up to 8. 11 and -3, in this case. Then you rewrite the quadratic as { 3x }^{ 2 }-3x+11x-11 From there, you...

Homework Statement Factor the polynomial x^2 - 4x + 4 -4y^2 completely. Homework Equations The Attempt at a Solution Rearranging, I get x^2 - 4y^2 - 4x + 4 Then, I know that it is equal to (x -2y)(x+2y) - 4(x-1) and that is my final answer. but, my teacher only considered the...

I'm teaching maths to myself so I don't really have anywhere else to go for an explanation other than here, so I apologise if this seems simple. How do you get from: (cos^2θ + sin^2θ)(cos^2θ - sin^2θ) to cos^4θ - sin^4θ NOTE: cos^2θ is shorthand for (cosθ)^2 as is with all the...

I tend to forget some of the trigonometric functions and someone showed me how to derive the double angle identities from what I think is Euler's formula: e^{ix} = \cos x + i\sin x = e^{i2x} = \cos 2x + i\sin 2x = (e^{ix})^{2} = (\cos x + i\sin x)^{2} I have a question about this step...I...

If I do this: \lim_{\alpha\rightarrow 0} \frac{sin\alpha}{\frac{2\alpha}{5}} = \lim_{\alpha\rightarrow 0} \frac{5sin\alpha}{2\alpha} = \lim_{\alpha\rightarrow 0} \frac{5}{2}\cdot \frac{sin\alpha}{\alpha} Am I allowed to do this? \frac{5}{2} \cdot \lim_{\alpha\rightarrow 0}...

Hey everybody I was wondering why when you factor an integral, the final answer, or area, is smaller than if you hadn't. Here's an example: \int\frac{x}{2x^2} - \frac{x}{2x} between 1 and 2. You would factor out \frac{1}{2} and bring it in front of the integral, right? But, my final...

Homework Statement http://alphacapitalist.com/wp-content/uploads/2012/06/factoringproblem.jpg Homework Equations / The Attempt at a Solution I tried factoring this but it seems to me that author has made an error somewhere. Either solution to this problem is not 1/a-1 or there is error in...

Solving linear differential equations by "factoring" I have thought of an interesting way of solving n-th order linear differential equations (with constant coefficients) by imitating the way we solve n-th order polynomials, that is by "factoring" it into a "product" of simple 1st order linear...

Alright, I am trying to work out some equations on a project to determine if fictional instances of physics are possible or not. In my case, I am seeing how a person travels if they are thrown from a jet that is traveling vertically (don't ask). I have completed the equations to solve how far...

Hi all. I'm trying to relearn S-plane analysis and filter transfer functions. What I'm having problems with is simple algebra i think, because it's been a while. Right now I've been reading http://www.ee.up.ac.za/main/_media/en/undergrad/subjects/eli220/polezero.pdf. What I'm confused about...

Homework Statement Hey, I am attempting to fully factorize z^{n}-1=0 for all integers of n where n does not equal zero, and where z is a complex number in the form a+bi. The question asks to first factorize the equation when n=3,4,5. I know how to factorize when n=3 and 4, but I get stuck at...

Homework Statement Factorise z^{8} -15z^{4} - 16 over the Complex numbers and Real numbers The Attempt at a Solution I factorised over the complex numbers, I'm not sure what they mean by over the real numbers. Do I substitute z = (x + iy) and then do it by expanding and separating...

2x^2+9x-5 here is the quadratic expression that I am trying to factor. Is there a way to factor this easily? I am getting confused on the signs. the book says the factor are: (2x-1)(x+5) but (-1)(2)+5=3 but why not (2x+5)(x-1)? and 5(2)=10-1=9 which looks like the correct answer...

I am trying to factor the following equation $$\large(x^{\frac{1}{n}}+a)^{n-1}$$ but the fact that the exponent is n-1 is throwing me off. How could I go about factoring out this equation? Thanks.

Hi, I am writing up a project based on an algorithm for factoring large numbers, I have reached seemingly simple point where I am stuck, I wonder if anyone can help me? I am trying to factor a large N such that N=pq for unknown primes p and q, I have described a method to find a value for...

now i found how to do the solution by doing an "Unorthodox" method of completing the square, could some one explain why the guy called it unorthodox? Solution: x^4 + 4 x^4 + 4 +4x^2 -4x^2 (completing the square) (x^2 + 4x^2 + 4) - (2x)^2 (x^2 + 2)^2 - (2x)^2 (x^2 +2 - 2x)(X^2 + 2 + 2x)...

Homework Statement Factor the following: 16z^2 - 9x^2 - 12xy - 4y^2 Solution of the problem is (4z - 3x -2y)(4z + 3x + 2y) The Attempt at a Solution I tried the following: 16z^2 - 9x^2 - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 12xy - 4y^2 = (4z - 3x)(4z + 3x) - 4y(3x + y) /i also...

I need to factorise 70 into primes, how do I go about this? So far I have 2,5,7 as primes in Z. So I suppose I need to factorise these in Z[i]? 2 = (1+i)(1-i) How do I go around doing the other two, is it possible that they're primes in Z[i]? Edit: I have a corollary where if p is a prime...

Hi all I saw the posting below in regards to nuclear not being all that its cracked up to be. This is from a scientist in europe. I am intersted in rebuttals. I am pro nuke and just entering the industry but I do not have the experience to shoot this down. Fishing for comments Post...

Homework Statement -19x^2-20x-9=0 The Attempt at a Solution With QF it looks like this: x=20+-(sqrt):1084/-38 How would I factor this without the QF?

Homework Statement 2n - 6m + 5n^2 - 15mn Homework Equations No particular equation since this is factoring The Attempt at a Solution Keep in mind that I struggle when it comes to grouping as I'm not sure where I'm supposed to start but... 2n - 6m + 5n^2 - 15mn Group first 2...

Easy factoring problem...I think Hi, So I'm working through how to do RSA encoding, but I've stumbled on something very simple in terms of factoring. All I pretty much want to know is: How do I factor: pq-p-q+1 To get: (p-1)(q-1) Expanding it isn't the problem...what little...

r,q are constants. I need to factor this equation such that there is a double root. -\frac{r}{q}u^3+ru^2-\left(\frac{r}{q}+1\right)u+r=0 Are there any tricks for this because this just a nasty equation. I don't know if that is a wise approach but: (au+b)(cu+d)^2 =...

I need to factor x5 - 1.I know (x-1) is a factor and have gotten: (x-1)(x4+x3+x2+x +1) I'm not sure where to go from here. Thanks in Advance.

Factoring a 4th order polynomial Homework Statement Example: (jw)^{3}+6(jw)^{2}+5jw+30=0 can be re-written into 6(5-w^{2})+jw(5-w^{2}). The fact that there are two identical (5-w^{2}) is a desirable outcome. Imaginary number j=\sqrt{-1} becomes -1 when raised to the power of 2. Homework...

Homework Statement I have a limit problem, however I do know how to work limits, I guess what I need is more of a refresher on how to work third degree polynomials. The polynomial(s) I am trying to work with are the following: x3-2x2+2x-15 -and- x3-5x2+10x-12 The limit is a limit where x...

Okay so I've been teaching myself (with the aid of the mighty internet & several friends) algebra & now calculus. I have found that I didn't do too good at high school for various reasons. Some good...some not good. Anyway... I have a (what is probably a basic question) about factoring limit...