Factoring Definition and 339 Threads

Homework Statement factor 4x^2-6xy+10y^2 Homework Equations The Attempt at a Solution completing the square i get, 4[(1/4)y^2-(3/4)xy+(9/16)y^2]-4(9/16)y^2+10y^2 but i don't know what to do with the bracketed term. It can't be factored easily

I had to factorise this formula. The answer that I came up with is below: 6ax - 12ay - 18a squared. 6(ax - 2ay - 3a squared) My book says that the correct answer is: 6a(x - 2y - 3a) Would my answer have been marked wrong in an exam? Why is the book's answer preferable to mine...

Homework Statement Can someone tell what are the other factoring methods when dealing with equations higher than the second degree. The only I is the synthetic division. Aside from that, I do not know anything. I need other factoring methods so I can deal with problems that cannot be...

Alright, I'll be honest. I was extremely tired and slept all through the lesson in Algebra today lol. And now I need help with factoring polynomials. Example problems that I need help on: 7h3+448 Perfect square factoring - y4-81 Grouping - 3n3-10n2-48n+160 You don't have to answer...

Homework Statement I need to find where these curves intersect: x+y = 2y^2 y = x^3 Homework Equations The Attempt at a Solution So I try to write both in terms of y, I get 2y^2 - y = y^(1/3) I try to factor 2y^2 - y - y^(1/3) = 0 y(2y - 1 - y^(-2/3)) = 0 ...

Homework Statement I need to factor this: u - u^6 -u^3 +1 = 0 Homework Equations The Attempt at a Solution I know that (u +1) and (u-1) are roots.. but not sure what to do now without long division.. Do I put them into multiples like (u^3 + 1)(u^3 -1) ??

Homework Statement I need to find where these intersect: y = |x| 3y - x = 8 Homework Equations The Attempt at a Solution I equate them: |x| = (1/3)x + (8/3) |x| - (1/3)x - (8/3) = 0 |3x| - x - 8 = 0 |2x| - 8 = 0 |x| = 4 Is that right? How do I get the other solution?

Homework Statement I need to find where these two intersect: x = y^3 x = 3y + 2 Homework Equations The Attempt at a Solution I set them to equate: y^3 = 3y + 2 y^3 - 3y + 2 = 0 How do I factor this??

Homework Statement I need to find the point at which these functions intersect: y = -sqrt(x) y = x - 6 Homework Equations The Attempt at a Solution I set them to equate: -sqrt(x) = x - 6 -sqrt(x) - x + 6 = 0 Now how do I find the root?

Homework Statement I am trying to factor x4+1 into two multiplied polynomials Homework Equations My teacher gave us this hint that its factored form is (ax2+bx+c)(ax2+bx+c) The Attempt at a Solution First i assumed that a and c were equal to 1 so that when x2 is multiplied...

Homework Statement 7X2(X - 2) - (X - 2) 2. The attempt at a solution Ok, this is really simple but for some reason I can't figure out why the answer has to be (7X2 - 1)(X - 2) The process is that I have to divide both parts by (X - 2). However, if I do that, I only get 7X2 - 1...

Homework Statement The polynomial f(z) is defined by f(z) = z5 - 6z4 + 15z3 - 34z2 + 36z - 48 Show that the equation f(z) = 0 has roots of the form z = ix where x is real, and hence factorize f(z)The Attempt at a Solution So I know that you begin by factoring out (z-ix) from the function...

Homework Statement The question is: Factor and Plot the polar equation r^2-r+(1/4)sin^2 4 theta Homework Equations N/A The Attempt at a Solution I have no idea how to do this.

ok so i was presented with the equation x^2-7x+12=0 and i can't decide what the answer should be. if i factor the equation i come up with 3 and 4. but when i plug those back into the original equation it doesn't work. so does that mean that there is no answer or does it mean I'm doing...

Imagine separating a parabola into its different x and y components and linking them by the component of time. Scenario: Given: Gravity No Drag The velocity of the launched object is not sufficient to escape the gravitational pull. Ignoring: The change of gravity as the distance...

Homework Statement x^4 + x^3 + 2x - 4 = 0 Homework Equations N/A The Attempt at a Solution x^4 + x^3 + 2x - 4 = 0 x(x^3 + x^2 +2) = 4 i don't know what to do with this. i tried to factor (x^3 + x^2 +2), but i don't know how. I also have a feeling that I am not doing this...

Homework Statement y\prime=4x^3+6x^2+2x+1 Homework Equations The Attempt at a Solution 4x^3+6x^2+2x+1 -1 = 2x(2x^2+3x+1) (I moved the +1 over so I don't get 1/x, but I figured this should screw up the equation since it is no longer 0 on the left hand side.) -1 = 2x(2x+1)(x+1) So the...

Consider this equation: 7x*tan(4x)=5x Initially, one might think to simply factor the x out of each side of the equation and be left with this: tan(4x)=\frac{5}{7} Well that's wrong! That is only one solution! The other solution is: x=0 You should instead have done the...

Homework Statement g(x)= x^4-2x^3-3x^2+2x+2 Homework Equations The Attempt at a Solution After using synthesized division, got x^3-x^2-4x-2 I need help in factoring from here please

Homework Statement Factor. 2x^{2}+5x-12 I just took a semester off from school and I feel dumb. My recommendation to anyone reading is don't do that. Anyways, back to gr. 10 math :cry: Normally if I was going to factor this I would try to eliminate the coefficient of x^{2} but it...

Homework Statement 8x^3 + 4X^2 - 2x -1 Homework Equations remainder theorem factor theorem The Attempt at a Solution None yet, not sure how to go about it when there is a coefficent in front of the highest power of X.

I'm currently taking a Math Analysis class. We started reviewing basic factoring from Algebra 2 before starting new material. I can factor a basic trinomial with the coefficient of x^2 being 1, but if the coefficient is 2 or more, I am not sure how to factor it. I am able to factor these very...

Homework Statement Factor 3x (4x-1)^-2 - 6x^2 (4x-1)^-1 Homework Equations The Attempt at a Solution

Homework Statement This is a limit problem but what I'm stuck on is algebra: find lim as u approaches 1 of ((u^4)-1)/((u^3)-1). Homework Equations The Attempt at a Solution 1 is a root and (u-1) is a common factor, so I want to rearrange the numerator and denominator so I can...

Homework Statement Factor 12X^3-12X^2-60X+24=0 Homework Equations The Attempt at a Solution

To what degree would proving the Riemann hypothesis facilitate the factoring of large composites? In other words, how much would a complete (as opposed to "hit-or-miss") knowledge of primes help to reduce the operations needed to factor large composites?

Homework Statement (4x-1)^{1/2}-1/3(4x-1)^{3/2}Homework Equations The Attempt at a Solution I think the GCF is (4x-1)^{1/2}. So, I get (4x-1)^{1/2}(1+(-1/3(4x-1))) = (4x-1)^{1/2}(-4/3x+4/3) = -4/3(4x-1)^{1/2}(x-1) However, the answer in the book is 4/3(4x-1)^{1/2}(x-1). I've done it several...

Hi, I use the \frac{-b \ \pm \ \sqrt{b^2 - 4ac}}{2a} formula to factoring the quadratic equation. Can anyone tell me how to factoring the cubic equation? Usually I use the division method to factoring higher order than quadratic equation such as cubic, etc., by trial, one-by-one. Cheers...

Why is it that a 16 comes out when you factor a 2 from each row of this matrix: 0 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0

*The subject should have been complex matrix square root. I need to find one solution to the follow set of complex equations: a*a+b*b = 1-K-K/2 a*b+c*d=K/2 c*c+d*d=1-K/2 where K is some real constant. This is equivalent to finding a 2x2 complex matric M such that M^\dagger M= 1-K-K/2, -K/2...

"Solving Equations by Factoring" - Find the length of the hypotenuse Homework Statement One leg of a right triangle is 2 feet more than twice the other leg. The hypotenuse is 1 foot more than the longer leg. Find the length of the hypotenuse of the right triangle. * I am not sure how to...

[b]1. Solve algebraically for... 1.) 4x*(x^2-5)+(x^2-5)^2=0 two separate problems not relating to each other 2.) 4x^3*(1-x)^3-3*(1-x)^2*x^4=0 [b]2. this symbol ^ is to the power of. all x's are the x variable as written in my precalc book. For problem 1. I see that...

Homework Statement factor -x^3 + 27 Homework Equations The Attempt at a Solution Nothing, I have no idea how to factor it.

Homework Statement can u factor x2+4 and can't seem to remember the the difference of cubes and isn't there another special cubed theorem. Homework Equations The Attempt at a Solution

Homework Statement I'm having trouble factoring this to its simplest term. I'm not very good at factoring, but I'm working on it. I was hoping that someone might be able to help me here. Homework Equations Find the critical points for f(t) = t * sqrt(4 -(t^2)) on the closed interval [1...

the question is this: factor the following polynomial with integer coefficients: x^{5024}+x^{1004}+1 my first thought is that since this polynomial doesn't have real roots such a factorization isn't even possible, but i really don't have any more clever idea how to factor this one.

Homework Statement A simple way to factor the left hand side of the given equation. Homework Equations E^2-E^2(\frac{\frac{F^2vt}{c}}{M})+(\frac{\frac{F^4v^2t^2}{c^2}}{M^2})=-p+(\frac{\frac{F^4v^2t^2}{c^2}}{M^2}) The Attempt at a Solution I would, just that i am confused on...

can you somehow factor the following equation ? sqrt(9sin^2(t)+16cos^2(t)+1/4)

Homework Statement I am stuck on these two pre-cal problems... can anyone help? Solve By Factoring: 2x^3 + 2x^2 = 4x + 4 This next one I have no idea how to do Find an equation of the cubic function whose graph passes through the points (3,0) and (1,4) and is tangent to the x-axis...

(x-y+2\sqrt{x}-2\sqrt{y})/(\sqrt{x}-\sqrt{y}) The first thing I did was group like terms (x+2\sqrt{x}-y-2\sqrt{y})/(\sqrt{x}-\sqrt{y}) Then from the liked terms I factored out a \sqrt{x} & -\sqrt{y} ((\sqrt{x})(\sqrt{x}+2)-(\sqrt{y})(\sqrt{y}+2))/(\sqrt{x}-\sqrt{y}) Here is where I...

Factoring problems... 1. Having problems with factoring almost got it except this 2 (3x^3+21x^2+36x)/ 3x^4+12x^3-27x^2-108x ( Edited) The Attempt at a Solution the numerator 3x^3+21x^2+36x I can see the factor right away its 3x so 3x(x^2+7x+12) and for new denominator that I mixed...

Does anybody have any good tricks to quickly factor a number in your head, or a trick that can be done quickly on paper? The best method that I know without using a calculator is the traditional method of finding two not-necessarily-prime factors and factoring those with the same method.

does anyone have a problem with the factoring function on the TI 89? i tried to factor (by using f2 factoring function)a simple problem like 12x^2+5xy-3y^2 the answer should be (4x+3y)(3x-y) but on my calculator i just get a rearranged order of 12x^2-3y^2+5xy...does anyone know how to fix this...

Homework Statement I am trying to find out when the denominator of this equation is zero so I can tell when the graph has asymptotes or holes. For squares I factor such as x2+2x-15 = (x+5) (x-3). How do I do that with a cube? Homework Equations (x-5) (x+3) X3-5x2+x-5

The question is as follows: \frac{lim}{h\rightarrow0} \frac{\sqrt{1+h}-1}{h} I don't know if the way I approached the question is right, I'll give you a step by step of what I attempted: First I converted the square root into 11/2 and h1/2 (can I do that? Is that correct?) Then I...

I have been trying this problem for a long time now. Factor the polynomial t^7+2t^6-24t^5. So far I came up with t^n(t+x)(t+y). I have no clue on how to work this out because i am only able to do them to the 2nd degree. I can really use the help. Thanks, Neil

factoring "puzzle" For what values of "a" can the following be factored and reduced: \frac {a^2 - 2x -3}{x^2 - 4x + a} Ok, so the first thing on the list is to factor the top term. x = \frac {-(-2) \pm \sqrt{(-2)^2 - 4 * 1 * (-3)} } {2 * 1} The roots are 3 & -1, and the factors then...

Homework Statement | x x^2 1 | | x^2 x 1 | | x^3 x^3 1 | The answer is = x^2(1-x)^2(1+2x) Homework Equations none The Attempt at a Solution By factoring the matrix step by step. Thanks :)

Is there a formula for factoring simple second order polynomials with zero trial and error? For example: 3X^2-11X+6 I know the answer is (3X-2)(X-3) and that can be checked by foiling obviously. I know 3X and X have to be the first terms, and that the last two have to be multiples of 6...

Homework Statement Solve the fallowing by factoring and making appropriate sign charts. 2x^2+4x\leq3 Homework Equations The Attempt at a Solution It simply does not factor the way I want it to(unless I did something wrong). I don't think it wants me to use the quadratic formula, and...