The volume of rectangular solid is x^3 +3x^2+2x-5) cubic cm and its height (x+1 )cm.what is the area of its base
divide
---- +x^2 +2x
x+1 | x^3 + 3x^2 + 2x - 5
----- x^3 + 1x^2
--------- + 2x^2 + 2x - 5
--------- + 2x^2 + 2x
remainder = -5
or
x^2 + 2x - 5/(x+1)
Since the volume is lwh, and we know h = x+1
then the base is lw
= (x^3 + 3x^2 + 2x - 5)/(x+1)
= (x^2 + 2x) - 5/(x+1)
I had expected the division to be exact.
Is there a typo?
The volume of a rectangular solid is (x^3 + 3x^2 + 2x) cubic cm, and its height is (x+1)cm. Whay is the area of the base?
Well, my dear friend, the area of the base of this rectangular solid can be found by dividing the volume by its height. However, since you have given me a polynomial function for the volume, I'm afraid the joke is on me!
You see, a polynomial function can have different values for different values of x. So, without knowing the value of x, I am unable to calculate the area of the base. It seems the math gods are pulling a little prank on us. They must be fans of practical jokes!
But don't you worry, my friend. I'm here to provide some laughter, even if the math gets a bit tricky.
To find the area of the base of a rectangular solid, we need to determine the dimensions of the solid. From the given information, we know that the volume of the rectangular solid is (x^3 + 3x^2 + 2x - 5) cubic cm, and the height is (x + 1) cm.
The volume of a rectangular solid is given by the formula: Volume = Length × Width × Height.
Let's assume that the length of the rectangular solid is L cm, the width is W cm, and the height is H cm.
From the problem, we can set up the following equation:
(x^3 + 3x^2 + 2x - 5) = L × W × (x + 1)
To solve for the length and width, we can rearrange the equation:
L × W = (x^3 + 3x^2 + 2x - 5) / (x + 1)
Now, we need to factor the cubic expression in the numerator to simplify further. The factorization of (x^3 + 3x^2 + 2x - 5) is:
(x^3 + 3x^2 + 2x - 5) = (x - 1)(x^2 + 4x + 5)
Substituting this factorization back into the equation, we have:
L × W = [(x - 1)(x^2 + 4x + 5)] / (x + 1)
Now, we can express the area of the base as:
Area of Base = Length × Width = (L × W)
Area of Base = [(x - 1)(x^2 + 4x + 5)] / (x + 1)
Therefore, the area of the base of the rectangular solid is given by the expression [(x - 1)(x^2 + 4x + 5)] / (x + 1) square cm.