Results 1 to 6 of 6

Math Help - polynomial expansion

  1. #1
    Junior Member
    Joined
    May 2005
    Posts
    25

    polynomial expansion

    one of the terms in the expansion (x+3)^7 is kx^5. determin the value of k.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Site Founder Math Help's Avatar
    Joined
    Apr 2005
    Posts
    171

    finding the pattern

    (x+y)^{1}=x+y
    (x+y)^{2}=x^{2}+2yx+y^{2}
    (x+y)^{3}=x^{3}+3yx^{2}+3y^{2}x+y^{3}
    (x+y)^{4}=x^{4}+4yx^{3}+6y^{2}x^{2}+4y^{3}x+y^{4}

    The pattern of coefficients is like pascals triangle, the outside is always 1's and you add the two coefficeints in the line directly above to get the inside ones:

    ...1 1
    ..1 2 1
    .1 3 3 1
    1 4 6 4 1

    As for the 3 (or y value see above) when you are talking about a power of 7 the power of the y will always be 7 - power of x in that part of the polynomial.

    Try to figure it out and post the solution if you can't get it or if you want me to check it I will give the answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2005
    Posts
    25

    i think i got it

    the next line would start with x^5 so the coefficient or the k value would be 1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Site Founder Math Help's Avatar
    Joined
    Apr 2005
    Posts
    171
    yes but the next line is to the power of 5, you are asking about power of 7. so the k you are after is actually different.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2005
    Posts
    25

    think i got it

    so then if it was like the trangle it would be like 7 chose 2 or 21
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Site Founder Math Help's Avatar
    Joined
    Apr 2005
    Posts
    171
    21 is correct but that is not k.

    you also need the 3 or y component.

    21*y^{2}*x^5
    or
    21*3^{2}*x^5
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. symmetry expansion of a polynomial.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: June 6th 2011, 04:15 PM
  2. Replies: 1
    Last Post: December 15th 2009, 07:26 AM
  3. Replies: 6
    Last Post: May 1st 2009, 11:37 AM
  4. Polynomial Expansion Using Pascals Triangle
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 3rd 2008, 08:29 AM
  5. [SOLVED] dividing polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 3rd 2008, 02:00 PM

Search Tags


/mathhelpforum @mathhelpforum