P(x) is a cubic and when divided by a quadratic will give a result with x = degree 1.
So I set P(x) = P1(x) * (axb) = P2(x) * (cxd), multiplied them out and equated coefficients of like powers.
The highest degree term and the constant term are easy. ax^3 = 2cx^3 give a = 2c and bk = dk (and here I assumed k<>0) give b = d.
Equating coefficients of x^2 gives d = 5c.
Plugging in these values and equating coefficients for x gives k = 30.
P1(x) = x^2 + x  30 = (x+6)(x5),
P2(x) = 2x^2 + 17x + 30 = (x+6)(2x+5),
(axb) = c(2x+5),
(cxd) = c(x  5),
and P(x) = c * (2x^3 + 7x^2  55x  150).

Posted by xdog
on 20130909 00:16:00 