# Thread: I NEED MAJOR HELP!(Question on Polynomials)

1. ## I NEED MAJOR HELP!(Question on Polynomials)

Ok so this is my tips question which is due tomorrow for marks and I havnt been able to think how to do it.

The Volume of a cylindrical can is
4(pi)x^3 + 28(pi)x^2 + 65(pi)x + 50(pi) cm^3. If the can has a height of
(x +2)cm, what is the radius of the cylinder? Now so far I figured the way to figure this out is to take the formula for Volume of a cylinder which is V=pi*r^2 *h and rearange is so your solving for r^2 instead so it would be r^2=(pi)(h)(V). The problem is im pretty sure I need to factor that equation out or expand w/e it is. I know how to expand out an equation where theres just x2 + x + 0 lets say but I dont know how to expand it when you have that extra x so its now x3 + x2 + x + 0. Can someone plz help me right now whoever's on at this time? Thanks!

2. Originally Posted by zarlock99
Ok so this is my tips question which is due tomorrow for marks and I havnt been able to think how to do it.

The Volume of a cylindrical can is
4(pi)x^3 + 28(pi)x^2 + 65(pi)x + 50(pi) cm^3. If the can has a height of
(x +2)cm, what is the radius of the cylinder? Now so far I figured the way to figure this out is to take the formula for Volume of a cylinder which is V=pi*r^2 *h and rearange is so your solving for r^2 instead so it would be r^2=(pi)(h)(V). The problem is im pretty sure I need to factor that equation out or expand w/e it is. I know how to expand out an equation where theres just x2 + x + 0 lets say but I dont know how to expand it when you have that extra x so its now x3 + x2 + x + 0. Can someone plz help me right now whoever's on at this time? Thanks!
$V = \pi r^2 h$

$\Rightarrow r^2 = \frac V{\pi h} = \frac {4x^3 + 28x^2 + 65x + 50}{x + 2}$

now, do polynomial long division (or synthetic division) to find $r^2$, then square root both sides when done

3. But what happened to the pi's within the equation for the volume?

4. Originally Posted by zarlock99
But what happened to the pi's within the equation for the volume?
i factored them out and canceled them with the $\pi$ in the denominator

5. So when I use synthetic devision i get this
x3 x2 x
-2| 4 28 65 50
-8 -40 -50
_______________
4 20 25 0 R=0

So would that be 4x^3 + 20x^2 + 25x + 0? Then how so I take the square root of that?

6. By the way, the answer is supposed to be 2x + 5, I just need to know how to get that answer.

7. Originally Posted by zarlock99
So when I use synthetic devision i get this
x3 x2 x
-2| 4 28 65 50
-8 -40 -50
_______________
4 20 25 0 R=0

So would that be 4x^3 + 20x^2 + 25x + 0? Then how so I take the square root of that?
no, you just divided, how would you end up with the same degree polynomial?

the answer is $4x^2 + 20x + 25$

now take the square root of that and that is r

8. ooooooooo I see, iunno but for some reason when I was looking through my notes I thought I saw after using synthetic devision u still stick with the x3, x2, and x but it never made sence, now i does tho. Thanks man a lot, u just saved me from losing marks.

9. well actually its not completely resolved unless the answer that was given is wrong. When I square root that I get 2x + 4.47 + 5, I got the 4.47 by taking the square root of 20x, but the answer that was given is (2x + 5)

10. Originally Posted by zarlock99
well actually its not completely resolved unless the answer that was given is wrong. When I square root that I get 2x + 4.47 + 5, I got the 4.47 by taking the square root of 20x, but the answer that was given is (2x + 5)
you cannot take square roots like that!

anyway, you just foil: $4x^2 + 20x + 25 = (2x + 5)(2x + 5) = (2x + 5)^2$

so $r^2 = (2x + 5)^2$

$\Rightarrow r = 2x + 5$