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05232011  #1 
Join Date: May 2011
Posts: 1

Division of Polynomials
Hi, nice to meet everyone, this is my first post and first maths question in this forum. I have a question that I am stuck and do not know what to do.
Here is the question: When P(x) = ax^3 + bx^2 + cx +d is divided by x + 2, the remainder is 5. Find a possible set of the constants a, b, c and d. 
05242011  #2  
Join Date: Dec 2008
Posts: 249

Quote:
a = 1 b = 6 c = 11 d = 1 A remainder is what is added (or subtracted) after all of a polynomials factors are divided. I got these by picking P(x) = (x + 1)(x + 2)(x + 3)  5, but you could just as easily choose (x + 2)(x + 2)(x + 2)  5, or almost anything else. From my first choice, then: P(x) = (x^2 + 3x + 2)(x + 3)  5 P(x) = (x^3 + 6x^2 + 11x + 6)  5 P(x) = x^3 + 6x^2 + 11x + 1 Another choice would be: a = 0 b = 0 c = 1 d = 3 for p(x) = x  3, since (x  3) divided by (x + 2) = 1 with remainder 5. Hope this helps. 

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