Need help withis Algebra question =S..

sofa kingcool

I need someone to go through how this algebra question is solved..
Please help!Thanks!:)

Solve the equation: 2x³ + 11x² + 4x - 5 = 0


f(-1)=0 , so (x+1) is a factor.(I understand this)


(It's this part I dont understand how to do!)

_____ 2x²_+_9x_-_5__
x+1/ 2x³ + 11x² + 4x - 5
_ 2x³ + 2x²_
9x² + 4x -5
_9x² + 9x_
-5x -5
_-5x-5_
0
(Dont understand this part either)

2x²+9x-5=(2x-1)(x+5)

2x³+11x²+4x-5=(x+1)(2x-1)(x+5)

(I know how these answers are got from above)
Solutions: x= -1 , x= 1/2, x= -5

Any help is great thanks!

Well, if (x+1) is a factor, you know that it should be divisible into the original polynomial. What you're doing then is dividing (x+1) into 2x^3 + 11x^2 + 4x -5; doing this will give you a quadratic equation (2x^2 + 9x - 5). You can then solve this using the quadratic equation formula (-b +/- ...). Which bit don't you understand: how to long divide algebra?

The second part is just letting the original polynomial equal its factors (You've worked out the factors using the factor theorem, and by long division and the quadratic formula).

If you want me to make it clearer just say.

sofa kingcool

-JammyDodger- wrote: »

Well, if (x+1) is a factor, you know that it should be divisible into the original polynomial. What you're doing then is dividing (x+1) into 2x^3 + 11x^2 + 4x -5; doing this will give you a quadratic equation (2x^2 + 9x - 5). You can then solve this using the quadratic equation formula (-b +/- ...). Which bit don't you understand: how to long divide algebra?

The second part is just letting the original polynomial equal its factors (You've worked out the factors using the factor theorem, and by long division and the quadratic formula).

If you want me to make it clearer just say.

Yeah it's the long division i really dont understand..
would you be able to explain how the long division is done to the
point where you end up with 0?
Thanks!

I think it would be far too difficult and tedious to attempt to explain long division on this, so the best thing you could do is to google "algebraic long division" or "polynomial long division". For, example http://www.mathsrevision.net/alevel/pages.php?page=1. Try to work through the examples given; and, with polynomial division, practise really does make perfect: it's the kind of thing that's very difficult to get without getting lots of practise. If you've any specific problems with it, feel more than free to ask here.

Dr.Millah

There is a great example of algebraic long division on this mans channel. Also some other handy videos which can be helpful to rember the basics of maths and mechanics problems.