polynomial

  1. C

    Polynomial Division Problem

    Polynomial Division Problem Calculate the following and state the remainder: 2x^3+x^2-22x+20 divided by 2x-3 Thanks!
  2. A

    Polynomial factorization calculator and root finder

    Hello folks. I have written a Web calculator that can factor polynomials and it can also find exact roots using rational numbers and radical expressions. You can enter any polynomial expression in the input box. You can see it at: http://www.alpertron.com.ar/POLFACT.HTM Currently, it can...
  3. S

    Cubic Polynomial Factorizing

    How is this equation in the attachment factorized? I need steps, please. Thank you in advance.
  4. idontknow

    Quadratic polynomial

    Find the quadratic equation which satisfies the condition x_1 x_2 =x_1 +x_2.
  5. M

    What is this question asking for? Polynomial

    Question: Find S as a polynomial in x where S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1 Understanding what is being asked here would be a useful first step:giggle: Do I need to expand the brackets or what? I understand a polynomial to be an expression involving sums of powers of a...
  6. romsek

    Some sort of extension to the polynomial remainder theorem?

    Two questions on another board I'd like to learn how to solve. 1) $p(x) \equiv 1 \pmod{x+1},~p(x) \equiv -7 \pmod{x+5}$ What is $p(x) \pmod{(x+1)(x+5)}$ ? 2) $x^{1000} \pmod{(x^2+1)(x+1)} = ?$
  7. A

    Factor polynomial

    Hello, When making some exercices to improve my general understanding of basic mathematics, I stumbled upon following problem: to factorise X^2 + ((sqrt 2)+(sqrt 3)) x + (sqrt 6) I do not recognise the form (a+b)^2, so I tried going for the discriminant, which would be ((sqrt 2)+(sqrt...
  8. Z

    Finding the roots of a 6-degree polynomial

    Hello, I am having trouble finding the roots of a 6-degree polynomial equation in expression form. I hope anyone can help reduce it to a form where the expression for each root can be determine. Thanks, ZeroKool
  9. H

    Polynomial help please

    Not sure where to start.
  10. M

    Finding polynomial of a given degree with given zeros: complext zeros

    I am stuck on this topic in pre-calculas class. I have practiced and read, watched videos and still stuck. Find polynomial f(x) of degree 4 with real coefficients and the follosing zeros -1,2,-3+i Thanks
  11. J

    Question about proving the availability of double real root of a polynomial

    For part b, it is assuming that n is an odd number, so r-a = r+a Since the exponent of n-1 would be an even number for n being an odd number, is the equation of (r-a)^(n-1) = -(r+a)^(n-1) undefined? It is because any real number to a power of an even number cannot be negative. Please...
  12. E

    Polynomial Factoring Question

    I am consistently getting answers that my book says are wrong, but only in terms of positive or negative signs, with every other thing composing my answer (parenthesis, exponents, coefficients and variables) being consistently correct. The following would be the best representation of what I...
  13. idontknow

    Polynomial solutions

    I'm not able to define the solutions. How many solutions does the polynomial equation below have for n natural? Note: (without complex solutions). \sum_{j=1}^{j=n} x^j =x^n+x^{n-1}+...+x^2+x=0
  14. SenatorArmstrong

    Cubic polynomial confusion

    Hello. I'm trying to find the fundamental matrix for a differential equation and I am getting completely stuck on this cubic polynomial. $(3-r)[(3-r)(-1-r)+3] -[(-1-r)+3] - [3-3(3-r)] = 0$ (this came from |A-rI| = 0) $\rightarrow -3(3-r) -3r(3-r)+r(3-r)+r^2(3-r) + 14 - 2r = 0$...
  15. B

    Matrices which satisfy the equation

    Show that there are no real 3x3 matrices which satisfy the equation (picture below), but there are complex 3x3 matrices and real 2x2 matrices which satisfy that. I know that this equation has no real roots, but I don't know how to apply that to matrices.
  16. A

    Irreducible or reducible polynomial?

    Hi all, I have used rational root test and obtain this result for the question: f(x) = 2x^4+8x^3+5x^2−7x−3=(2x^2+2x−3)(x^2+3x+1) This shows that there is no linear factor but a quadratic factors instead. Do I still consider such polynomial as reducible or irreducible? Am I...
  17. A

    polynomial

    I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.
  18. B

    Sign changes in computing Quartic function

    Ferrari method uses simpler cubic equation. For complex coefficients: (0.75, 1.25)x^4 + (1, 0)x^3 + (-1.25, 0)x^2 + (1.5, -0.25)x + (1.75, -1) p=(-0.358131487889273, 0.891003460207612), q=(0.203643395074293, -1.232139222471), r=(0.16504232468481, -1.24136744052394) cubic: (1, 0)z^3 +...
  19. Monox D. I-Fly

    [ASK] About Polynomial

    A polynomial f(x) = 2x^3-5x^2+ax+18 is divisible by (x - 3). The result of that polynomial f(x) divided by (x - 1) is .... A. 2x^2-7x+2 B. 2x^2+7x-2 C. 2x^2-7x-2 D. x^2-6x-2 E. x^2-6x+3 I got a + 3 = -6 and so a = -9 and f(x) = 2x^3-5x^2-9x+18, but when I divided it with x - 1 I got...
  20. C

    relation between order of polynomial fit and range of x data

    Hi everybody, I have y-data that span an x-data range of say 1:100. The data are nicely fitted with a polynomial fit of 3rd order (Matlab/python: polyfit(x,y,3)). I have a second set of y-data (say: yy), spanning only half of the data range, say x=51:100. Is there any reasonable...