Aug 23, 2022

# Box problem (Cubic polynomial)

hey guys i just want to make sure i make a video on this question. I know in the past you may have had trouble with word

### problem

s, so I want to make sure you start with this question. so if you please make sure you start by reading the question and what it is asking you to do. here we have a box with the top open. Starting with a piece of cardboard that measures 14 by 12 inches, the first step I would recommend if you don't have the sketch. I would say go ahead and draw what they tell you to do.
In this case, we already have it. a sketch, so let's go ahead and add those labels of our 14-inch by 12-inch info. I would absolutely go ahead and use the longest side to represent that 14 inches and excuse my horrible on straight lines but this here represents that between this line and the end of the other line for my cardboard the length is 14 inches the other side or my short side between here and here the length is 12 inches in the

### problem

it says you would cut a square piece out of each piece of that cardboard so you can fold it into an open top box like the picture shown here ok the dimensions of our box will be a height of X, where X represents the length of this little piece of square that we are going to cut from each corner, we also have length and width for that box, let's go back to an unfolded box and see what the dimensions are for the length and width for the length we start with 14 inches long and then cut two little squares with dimensions of X since we are cutting these two ex so the length we can mark inside here it's 14 minus 2x we can do the same thing with the width the width will be the initial 12 minus the 2x lengths we're going to cut the width will be 12 minus 2x now that we have this sketch completed we're going to go ahead and read exactly what it tells us ask us to do we want to find what is the length of this square or what is the value of x if we know the volume of the box is 144

#### cubic

inches it might be helpful to review how we find the volume of the box the value is equal to length times width times height ok in this case let's go ahead and write this in function notation so we have f of X the function of X is equal to length times width times height let's replace each of these values ​​with their equivalence the length of my box this edge here equals this edge here so we have 14 minus 2x the width of the box is equivalent to this edge we have 12 minus 2x and then the height of the box equals the length of that square we're looking for equals X this and looking for the value of x when the volume is equal to 244 that means I'll be solving the equation of 144 this will be the value of my function 144 equals 14 minus 2x times 12 minus 2x times X I won't be solving the complete solution here at the video and this is enough to get you started clearly you will have a

#### cubic

function and to be able to solve that function you need to multiply everything until you get 144 on one side and then set it to equal to zero hopefully the

### problem

is solved well with grouping and, if not you can always graph that function and see what its real solutions are, you can also find the complete solution in the

### problem

solved in degree good luck guys
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