Can someone please help me with a polynomial function problem? Since my pre-cal final is after this holiday break, my teacher gave us a study packet to work on and turn in once we return. After two days I've finished 199 out of the 200 problems. And i'm stuck on this one problem.

A candle mold shaped like a rectangular prism has a square base. Its height is 5 centimeters longer than its width. The mold has a volume of 144 cubic centimeters. How wide is the mold?

I don't even know where to start D: Pre-cal is by far my worst subject.

Question

Can someone please help me with a polynomial function problem? Since my pre-cal final is after this holiday break, my teacher gave us a study packet to work on and turn in once we return. After two days I've finished 199 out of the 200 problems. And i'm stuck on this one problem. 

A candle mold shaped like a rectangular prism has a square base. Its height is 5 centimeters longer than its width. The mold has a volume of 144 cubic centimeters. How wide is the mold?  

I don't even know where to start D: Pre-cal is by far my worst subject.

cwrw238 · Answer

let x be the width of the base 
then the height = x+ 5

cwrw238 · Answer

the volume of the prism = w^2h
where h = height and w = width 
so now you can form an equation and solve for x

cwrw238 · Answer

w = x and h = x + 5
so we have 
volume = x^2(x + 5) = 144
solve this for x

directrix · Answer

@TeacupsAndMigranes     Do you know or have you heard of the Rational Root Theorem?

I'm asking because you will need to solve x^3 + 5x - 144 = 0 for x.

anonymous · Answer

I believe so. That's the x=p/q thing, correct? Where it's the ratios of the factors of constants? And... the leading coefficient?

directrix · Answer

Correct.

anonymous · Answer

So use that on x^3 + 5x - 144 = 0 and I'll be able to find X?

anonymous · Answer

So my constant term is 144 and my leading coefficient is 1?

directrix · Answer

Yes.

Take the factors of 144 and place them over the factors of 1 and remember that they could be positive or negative.

directrix · Answer

Because the leading term is x^3, you can tell that whatever the root is, it has to be fairly small because you are cubing it.

directrix · Answer

For example, 72 is a candidate from the RR Theorem, but once you cube 72, you can tell it is too big to go to zero when added to 5*72 and -144.

directrix · Answer

Ask a question if you want to.

anonymous · Answer

The factors I believe are right is 1,2,3,4,6,8,9,12,16,18,24,36,48,72, and 144. (negative and positive.)  So I would plug one of those numbers in for X and see if once solved it would equal 0?

directrix · Answer

Yes. If polynomial equation has one or more rational roots, then they will come up.

anonymous · Answer

Okay, great! Thank you so much for the help! :D