Question

How do you write a polynomial for the volume of a prism if the dimensions are 8x-4 by 2.5x by x?

Answer 1

Prism Volume `=20x^3-10x^2`

Explanation:

According to Wikipedia , " a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables ." This could include expressions such as `x+5` or `5x^2-3x+4` or `ax^3+bx^2+cx+d=e`.

The volume of a prism is generally determined by multiplying the base by the height. For this, I'm going to assume that the given dimensions relate to the base and height of the given prism. Therefore, the expression for the volume is equal to the three terms multiplied by each other, which gives
`(8x-4)(2.5x)(x)`
`=(20x^2-10x)(x)`
`=20x^3-10x^2`

Here we have our polynomial, which we can turn into an equation by declaring that the volume of the prism is equal to it, or
`V=20x^3-10x^2`. For real solutions of this equation, we plot this into a graph like below,
graph{20x^3-10x^2 [-2.5, 2.5, -1.302, 1.303]}
which shows that there are real-life applicable solutions for this equation when `x>0.5`

I hope I helped!