1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polynomial factor help

  1. Dec 12, 2008 #1


    User Avatar
    Homework Helper

    1. The problem statement, all variables and given/known data
    A polynomial [tex]P(x)=(x-b)^7Q(x)[/tex]
    a) Show that [tex]P(b)=P ' (b)=0[/tex]
    b) Hence find a and b, if [tex](x-1)^7[/tex] is a factor of: [tex]P(x)=x^7+3x^6+ax^5+x^4+3x^3+bx^2-x-1[/tex]

    2. Relevant equations
    If [tex]P(x)=Q(x)R(x)[/tex]
    Then [tex]P ' (x)=Q ' (x)R(x)+Q(x)R ' (x)[/tex]

    I can't think of anything for the factoring aspect of the question.

    3. The attempt at a solution
    For a)
    [tex]P ' (x)=7(x-b)^6Q(x)+(x-b)^7Q'(x)[/tex]

    But for b) I have no idea how to apply anything from a) to answer the question. Any ideas?
  2. jcsd
  3. Dec 12, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    Re: Factors

    Well if [itex](x-1)^7[/itex] is a factor, then you can write P(x) in the form: [itex]P(x)=(x-1)^7Q(x)[/itex]....So P(1)=__? and P'(1)=___?

    But what are P(1) and P'(1) for [itex]P(x)=x^7+3x^6+ax^5+x^4+3x^3+bx^2-x-1[/itex]?:wink:
  4. Dec 12, 2008 #3
    Re: Factors

    From P(1) and P'(1) you will get a simultaneous equation whereby a+b=? and 5a+2b=?
  5. Dec 12, 2008 #4


    User Avatar
    Homework Helper

    Re: Factors

    Ahh since [tex]P(1)=P'(1)=0[/tex] and by finding [tex]P(1)=6+a+b[/tex] and [tex]P'(1)=37+5a+2b[/tex] from substituting into the equation, I find a and b through simultaneous equations. Thus, [tex]a=-8\frac{1}{3},b=2\frac{1}{3}[/tex]
    I really hope I can pick these ideas up in the test...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Polynomial factor help
  1. Factoring Polynomials (Replies: 2)

  2. Factoring Polynomial (Replies: 4)

  3. Factoring a polynomial (Replies: 4)