Math Is Fun Forum

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

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