polynomials

  1. R

    Polynomial division with remainders, could someone help, please?

    Let f(x) = x^4+px^3+qx+5, where p, q are constants. The remainder when f(x) is divided by (x+1) is 7, and the remainder when f(x) is divided by (x-2) is 1. Find the value of p and the value of q. Could someone solve it, please? I've been stuck on this problem for over two hours...
  2. L

    Trouble finding 5th degree polynomials with the Casio fx-991EX Classwiz

    In class, my math instructor showed us how to find 5th degree polynomials on the classwiz, but I don't remember how to do it and keep messing up. I think he either input something like Ax5+Bx4+......C then input the values for A, B, etc and found x like that. Or he somehow used the spreadsheet...
  3. N

    How to find rational roots for a cubic polynomial?

    Hi there, I want to find the x intercept for the function y= x3-9x2+15x+30. The answer from the graphing calculator is x=-1.133. I am aware of the factor theorem and the rational factor theorem (for an integer other than 1 or 0 as a leading coefficient). But in this case neither of these can...
  4. K

    polynomials need ASAP

    construct a polynomial with the following properties: Third degree, zeros at 1,2,3, and passes through the point (4,12)
  5. O

    Domain and polynomial degree

    Hi, I hope someone can help. So I have the following function h(x) = f(x)\cdot (1/f(x)). I'm trying to understand if the degree in the function changes why the domain would be different. For example, let's say that f(x) = (x^2)-25...the domain for h(x) would be all real numbers such that x...
  6. O

    Solving inequalities

    Hi, I hope someone can help. So I have solved the following inequality in a very specific way: I'm wondering whether there is a way to remove the denominator from a rational inequality while still providing the same solutions (i.e. -1 < x <3 or x >= 7)? All I know is that it is "bad" to...
  7. O

    Combining rationals and creating a function

    Hi, I hope someone can help. I want to know whether there is any rationale behind my textbooks solution for combining rationals to create a function. In all the solutions in question 3 (which I have attached), the rational on the right-side is always brought to the left-side. For example, 3d's...
  8. O

    End behaviour of a rational function

    Hi, I hope someone can help. I'm trying to understand why in this example does x approach -3 from the positive direction starting at the interval of -2? Why doesn't it, for example, begin at -1? Here's also a link to the video...
  9. J

    Find an n^{th} degree polynomial with real coefficients satisfying given conditions.

    MSU College Algebra Help: Find a nth degree polynominal with real coefficents satisfying the given conditions. n=4, 6i and -8i are zeros, and f(-1)=2405. I got -8(x^3)i+64x^2-(288x)i+2303. This is marked as wrong in "WeBWorK". Please help!
  10. T

    Finding HCF of two or more polynomials

    Hi all, I was reading a book and I got to this but I don't really understand how the author done this, could someone please explain it to me. Thank you
  11. A

    quartic polynomials

    Hi; If quartic polynomials meet the right criteria we can factor using the rational root theorem and on from there. How can you tell if a quartic polynomial is factorable in the first place and if not what method do I use? Thanks.
  12. E

    Factorisation of Polynomials

    Hi everyone! I am quite confused about the 'Factorisation of Polynomials' (Wondering) For example: ​Without dividing, find the remainder when the first polynomial is divided by the second: 1) x^3 - x^2 - 3x + 1, x -1 2) 108x^3 - 27x^2 - 1, 3x + 1 How would you work these out? Any help much...
  13. E

    Long Division with Polynomials

    Hi everyone! I am VERY confused on how to do long division with polynomials!! Here is an example: 3x^3- 4x^2+ 2x +1, x+2 Any help would be much appreciated! Thank you in advance :) ~EbonyJade :)
  14. C

    Division of Polynomials

    Hi I AM EXTREMELY CONFUSED RIGHT NOW! Could someone please explain simply to me how to do the division of polynomials? I have no previous knowledge of long division using polynomials so could you please explain it to me as simply as possible? x^3+x^2-2x+3, x-1 Thank you SO much!!!!!!!! :)
  15. K

    Predictor Corrector method with lagrange polynomials

    Hello! I have to build a predictor corrector method for y' = f(x,y) with the following information. Predictor: integrate the differential equation over (Xk,Xk+1). Approximate f(x,y) by a first order Lagrange interpolating polynomial based on the points Xk-2 and Xk-1 Corrector: integrate the...
  16. Y

    LCD of Polynomials

    I have a mind stretcher I cannot figure out. Consider the rational expressions P/Q and R/S, where P,Q,R, and S are polynomials. Under what circumstances will the LCD of the rational expressions be equal to the product of the individual denominators QS? Give examples to support your answer...
  17. M

    Symmetric Polynomials Involving Discriminant Polynomial

    Question: Let τ = (i, j) ∈ Sn with 1 ≤ i < j ≤ n. Prove: δ(rτ(1) , . . . ,rτ(n) ) = −δ(r1, . . . ,rn) Note: Discriminant Polynomial δ(r1,r2,.....,rn) = ∏ (ri - rj) for i<j I am pretty confused on where to begin. Based on the note, does −δ(r1, . . . ,rn) then =...
  18. R

    Abstract algebra Polynomials and Prime

    Let g(x) ∈ ℤ[x] have degree at least 2, and let p be a prime number such that: (i) the leading coefficient of g(x) is not divisible by p. (ii) every other coefficient of g(x) is divisible by p. (iii) the constant term of g(x) is not divisible by p^2. a) Show that if a ∈ ℤ such that [a]_p ≠...
  19. B

    Polynomials with fractional exponents

    I have to solve for x in each of these equations. Help would be appreciated. (x^2/5)+(3x^1/5)+2=0 I tried increasing both sides to the 5th power to solve this, but I came up with some answers that I don't think are correct. (x^1/2)-(13x^1/4)+36=0 My only idea for solving this one is to...
  20. A

    High order polynomials

    Hello I am working on high order polynomials and I have two questions: 1. Is there a method other than the one based on the "synthetic division with testing the signs" for identifying the lower and upper limits of the real roots? 2. Is there a way for identifying the smallest interval on the...