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Math Help - Polynomial (evaluation - multiplication - interpolation)

  1. #1
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    Polynomial (evaluation - multiplication - interpolation)

    Hello, I have no idea on how to solve this problem:
    Given the polynomials A=x^3 +2x -1 , B=x^2-x+3 evaluate them for x=-2:1:3
    and calculate their product and its coefficients.
    I need another way on doing this, instead of calculating A and B one by one
    (I shouldn't use the simple method ie. x=-1: A_{-1}=(-1)^3 +2(-1) -1= -4 ....).
    How can this be done? Thank you.
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  2. #2
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    Why should you not use the "simple" method?

    If you really want to do it "the hard way", you can use "synthetic division":

    -2) 1 0 -2 -1 ("1 0 -2 -1" are the coefficients of [tex]x^3- 2x- 1)
    -2 4 -4
    1 -2 2 -5 so A(x)= -5

    where I brought down the first "1" to the third row then multiplied it by -2 to get the -2 in the second row and added it to 0 to get -2 in the third row, multiplied that by -2 to get the 4 in the second row, add that to -2, etc.

    To multiply A and B, use the "distributive law":
    (x^3- 2x- 1)(x^2- x+ 3)= x^3(x^2- x+ 3)- 2x(x^2- x+ 3)- 1(x^2- x+ 3) and distribute again: (x^3)(x^2)- (x^3)(x)+ (x^3)(3)- (2x)(x^2)+ (2x)(x)- (2x)(3)- (1)(x^2)- (1)(x)+ (1)(3)
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  3. #3
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    Hello and thanks for your answer.
    I shouldn't use the simple method because we need a faster way on doing this
    (for example, when the calculations are made by a computer
    it is too slow to calculate them for a wide range of values).
    I think that a way to evaluate the polynomials makes use of matrices,
    the results are correct but I don't know if this is an efficient way.

    This is how I have done it (see attachment)

    I have done the same hor B(x) and again the results are correct.
    I now have to do the multiplication and interpolation...
    Attached Thumbnails Attached Thumbnails Polynomial (evaluation - multiplication - interpolation)-untitled2.jpg  
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