2006-03-08T10:50:27ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=3094I did this question 3 times seperately, each time I made the same mistake. (3)^3 = 27 as you state in the first line, I put down 9 each time!!!]]>http://www.mathisfunforum.com/profile.php?id=20032006-03-08T10:50:27Zhttp://www.mathisfunforum.com/viewtopic.php?pid=30765#p30765Since f(3)=0, 27+9a+3b+c=0,...(1) f(-2)=-40, therefore, -8+4a-2b+c=-40....(2) Since c=0, 9a+3b=-27...(3) 4a-2b=-32...(4) 18a+6b=-54 12a-6b=-96 30a=-150, a=-5, b=6.
***I think....I haven't double checked my answer****
]]>http://www.mathisfunforum.com/profile.php?id=6822006-03-08T10:45:33Zhttp://www.mathisfunforum.com/viewtopic.php?pid=30761#p30761so if f(3) = 0 and f(-2) = -40, what are the values of a and b? I've been bearing in mind that c = 0 to work this out but I always end up with fractions in my answer, the book says a and b are integers.]]>http://www.mathisfunforum.com/profile.php?id=20032006-03-08T10:03:57Zhttp://www.mathisfunforum.com/viewtopic.php?pid=30753#p30753The factor theorem states that a polynomial f(x) is divisible by (x-a) if f(a)=0. The given polynomial is
Since it is divisible by x, it follows that f(x)=0, therefore, the given polynomial is equal to zero, and c=0. True, because, if c is a non-zero constant, the polynomial is not divisible by x. ]]>http://www.mathisfunforum.com/profile.php?id=6822006-03-08T09:18:44Zhttp://www.mathisfunforum.com/viewtopic.php?pid=30746#p30746I have an expression: f(x) = x^3 + ax^2 + bx + c which is divisable by x. Does this mean that f(0) = (0)^3 + a(0)^2 + b(0) + c = 0 and thus c = 0?]]>http://www.mathisfunforum.com/profile.php?id=20032006-03-08T08:50:49Zhttp://www.mathisfunforum.com/viewtopic.php?pid=30707#p30707