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RickyOswaldIOW
2006-03-08 21:50:27

I 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!!!

ganesh
2006-03-08 21:45:33

Since 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****

RickyOswaldIOW
2006-03-08 21:03:57

so 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.

ganesh
2006-03-08 20:18:44

The 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.

RickyOswaldIOW
2006-03-08 19:50:49

I 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?