Math Is Fun Forum

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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Aloha Nui means Goodbye.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

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.

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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.

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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Aloha Nui means Goodbye.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

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****

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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.

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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Aloha Nui means Goodbye.