This one is really wrecking my head. I've been working on this for hours and I just can't seem to get the correct answer. I'm starting to think there is an error in the textbook, but I've been studying for hours and I think I may just be losing my focus.
The question is:
Find the value of p and the value of q if px^3 + qx^2 - 58x -15 is divisible by x^2 + 2x -15.
So, I've broken the factor down into roots, namely (x + 5) and (x - 3). Using the factor theorem, if f(x) = px^3 + qx^2 - 58x -15, then f(-5) and f(3) should both be equal to 0, right?
However I've tried and tried and I just can't get the correct values for p an q, which are given as 4 and 9, respectively.
p(-5)^3 + q(-5)^2 - 58(-5) -15 = 0
p(-125) + q(25) + 290 -15 = 0
-125p + 25q + 275 = 0
25q + 275 = 125p
q + 11 = 5p
q = 5p - 11
p(3)^3 + q(3)^2 - 58(3) -15 = 0
27p + 9q - 174 - 15 = 0
27p + 9q - 189 = 0
27p = 189 - 9q
3p = 21 - q
p = 7 - q/3
now, express q in terms of p
p = 7 - (5p - 11)/3
3p = 21 - 5p -11
8p = 10 or p = 10/8 or 1.25. But p should equal 4???
I have done this over and over and over and over and I just can't get the correct values for p and q. Can someone please tell me where I'm going wrong?
Thank you. You will be saving me from total brain meltdown.