March 31, 2015

Homework Help: Factoring Polynomials (need HELP!!!)

Posted by Emily on Wednesday, January 10, 2007 at 11:24pm.

Ok, this is pretty long, so bear with me.
The problem says:
The diagram (not shown here, sorry) shows a cube of metal with a cylinder cut out of it. The formula for the volume of a cylinder is V=pi*r^2*h, where r is the radius and h is the height.
The cube's length, width, and height is 4s for each one of them. The cylinder's radius is s and the height is 48 inches.

a. Write a formula for the volume of the cube in terms of s. I got V=(4s)^3
b. Write a formula for the volume of the cylinder in terms of s. I got V=pi*s^2*48
c. Write a formula in terms of s for the volume V of the metal left after the cylinder is removed. So wouldn't it be [volume of cube]-[volume of cylinder]=V? If so, I got (4s)^3-pi*s^2*48=V. Is this correct? If it isn't, then that would explain my problem for this next one...
d. Factor your formula from part (c). I couldn't find out how to factor this one out. No other numbers in the polynomial can be divided by pi evenly, so what do I do?
e. Find V in cubic inches for s=15 in. I haven't gotten to this one yet, but I'll probably figure it out soon.

I really need help!! I need it for my homework that I will eventually have to turn in and I will lose a LOT of points if I don't do every problem. Somebody plz clear this up (no one has been able to yet), I'll GREATLY appreciate it!

a and b are correct
c) V = (4s)^3 - pi*s^2*48
= 64 s^3 - 48 pi s^2
= 16 s^2 (4 s - 3 pi)

d) Plug s = 15 into the above equation for the answer

Thank you very much! I really appreciate your help!

Help Me Woodie!

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