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Forcing a Polynomial Factor (Posted on 2013-08-03) Difficulty: 3 of 5
Find the values for a and b to force the polynomial x10 + ax5 + b to have x2+2x+3 as a factor.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (1 votes)

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re: Another approach | Comment 3 of 4 |
(In reply to Another approach by Steve Herman)

I used Steve Herman's other approach doing a very tedious long division.

The final remainder was:

(-11a + 22)x + (-12a - 219 + b)
Which leads to:
a=2
b=243
which agrees with the first solution, by Daniel.

Also, in the quotient obtained by long division, the coefficients for the powers higher than x^3 came out just as in Daniel's solution.  After that:
(a+10)x^3 + (13-2a)x^2 + (a-56)x + (4a+73) i.e. with same answer, only in terms of "a"


  Posted by Larry on 2013-08-04 20:05:43
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