00:01
In this question, we are told that the height of a square based box is 4 centimeters more than the side length of the base.
00:08
This means that the base of the box is square and height is 4 more, right? if the length of the base is x, then the height equals to x plus 4.
00:21
We are also told that the volume equals to 255 cubic centimeters.
00:26
Recall that the volume of a box is the area of the base, and since the base is a base is square its area is x squared multiplied by height so the volume is x squared times h on the other hand the volume equals to 225 we also know that h equals to x plus 4 so if we replace h by x plus 4 we are going to get x squared times x plus 4 equals to 225 this gives us a cubic equation x cube plus 4 x squared equals to 225 or we're going to write this as x cube plus 4x squared minus 225 equals 0.
01:29
Now we need to solve this equation.
01:33
To find to solve this equation we have to guess the first root and the guess the root must be divisible.
01:46
225 must be divisible by the root.
01:49
225 is not divisible by 2.
01:53
It is divisible by 3, but let's try x equals 5.
01:57
My first guess would be x equals 5.
02:00
We are going to get 5 cube plus 4 times 5 squared minus 225 equals to 0.
02:09
Equals, we don't know yet if it's 0.
02:13
This equals to 5 cube equals to 125.
02:18
5 squared.
02:19
Word is 25 and 4 times 25 is 100 and 125 plus 100 minus 225 equals to 0 which means that x equals 5 is root of this equation 0 of the equation and this means that we can find we can divide the polynomial by x 5 x minus 5 using long division so what we are going to do now is we will divide x cubed plus 4 x squared minus 225, we will divide this by x minus 5.
03:13
We will divide x cube by x.
03:16
If we divide x cube by x, we are going to get x squared.
03:21
Then we will multiply x squared by x minus 5 and subtract it.
03:28
X squared times x minus 5x squared equals to x cube minus 5x squared...