Math Is Fun Forum

ahgua

Member

Registered: 2005-08-24

Posts: 25

Factor and Remainder Theorem

Given that (2x + 1)(x – 1) are factors of a cubic expression g(x).  When g(x) is divided by x²  − 2x – 3 ,  it leaves a remainder (31x + 33).  Find the expression g(x).

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factor and Remainder Theorem

Hi ahgua;

You are right in calling g(x) an expression because I can find no cubic polynomial with those properties. Here is what I do have.

Notice this is not a polynomial. But it is an expression with a cube. Being that it has 4 roots it behaves more like a quartic.
That is why I prefer this expression.

It has 3 roots and behaves like a cubic in that regard.

I am still working on hopefully a better solution.
Both of the above will leave a remainder of 31x + 33 as required.
Since you did not specify that you were looking for a cubic polynomial just a cubic expression the above answers might be what you want.
Need more info to do better.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Factor and Remainder Theorem

Hi ahgua

I agree with bobbym.  There's no cubic that I can find with these properties.

Any chance there's a typo error with the problem.

I found 

which has (2x+1) and (x-1) as factors and a remainder of 13x +3 when divided by the quadratic.

Please check your problem for us.  Thanks.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob