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#1 2018-04-27 05:21:53

Mercurus
Guest

Algebra, factor and remainder theorem

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.

#2 2018-04-27 18:56:59

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,382

Re: Algebra, factor and remainder theorem

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

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#3 2018-05-08 20:02:34

Grantingriver
Member
Registered: 2016-02-01
Posts: 95

Re: Algebra, factor and remainder theorem

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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#4 2018-05-08 20:13:47

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,382

Re: Algebra, factor and remainder theorem

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

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#5 2018-05-08 20:25:45

Grantingriver
Member
Registered: 2016-02-01
Posts: 95

Re: Algebra, factor and remainder theorem

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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