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**Mercurus****Guest**

Please assist on this problem: When f(x) = 2x^3 +4qx^2 - 3q^2x - 2 is divided by x-q, the remainder is 10.

Calculate the value of q.

I have tried to factor the polynomial and dividing by x-q.

I am missing something here.

Thanks.

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,442

hi Mercurus

Welcome to the forum.

Got to go out so this will be a quick hint.

Try the remainder theorem: http://www.mathsisfun.com/algebra/polyn … actor.html

I think that will do it.

Bob

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 Bundy

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 106

If you divide 2x³+4qx²-3q²x-2 by x-q you will get 3q²-2 and from the information in the question you will have:

3q²-2=10 ⇒ 3q²=12 ⇒ q²=4 ⇒ q=±2

That’s it.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,442

hi Grantingriver

I've tried this two ways (remainder theorem and 'long division' and both ways get 3q^3 = 12*. I was expecting a simpler value for q. Where am I going wrong?

* cubed not squared ???

Bob

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 Bundy

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**Grantingriver****Member**- Registered: 2016-02-01
- Posts: 106

Hi bob bundy, sorry you are right I have made a mistake. Here is the correct solution:

If you divide 2x³+4qx²-3q²x-2 by x-q you will get 3q³-2 as a remainder and from the information in the question you will have:

3q³-2=10 ⇒ 3q³=12 ⇒ q³=4 ⇒ q=∛4

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