Question
I havethis word problem:
The heightof a box containing the HP Laser Jet III printer cartridge is 4 in.more that the width and the length is 1 in. more than the width. Ifthe volume of the box is 630 in. cubed, then what are thedimensions of the box.
I solvedit like this:
Equation:
V= L * H* W
Solution:
V= (1+w)(4+w)(w)
630= (1+w)(w)(4+w)
630=w3+5w2+4w
w3+5w2+4w-630=0
w = 7.0
I justplugged the equation into the calculator to get the answer Igot.
Myquestion is how would I go about factoring thisw3+5w2+4w-630=0
had I not put it in the calculator?
Explanation / Answer
The eqn you are asking about does NOT factor usingintegers. Moreover, the soln you got, w = 7 , is not quite right sincein this problem w is not an exact integer. The soln forw is CLOSE to 7, but it is not exactly 7. I got x= 7.0628821 If you graph your eqn, the soln "appears" to be 7, but it isnot exactly 7. To find the root (aka the zero) exactly, the graph by itselfdoes not do the job. What you need to do on yourcalculator is the follows: 1. make graph of the eqn to solve; change standardwindow to something like ymin = - 700, and ymax = 700. 2. hit 2nd trace to get into the "calculate"mode 3. choose choice 2 "zero" from the menu 4. place cursor as requested on screen to left of theroot, to the right of the root, and then very close to theroot. 5. Your screen gives you the exact root of7.0628821