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#1 2006-03-07 20:50:49

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Factor X

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?


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#2 2006-03-07 21:18:44

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,956

Re: Factor X

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. smile


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2006-03-07 22:03:57

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Factor X

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.


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#4 2006-03-07 22:45:33

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Factor X

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****


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2006-03-07 22:50:27

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Factor X

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!!!


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