Respuesta :
Answer:
Step-by-step explanation:
6x^3 - 3x^2 - 45x = 3x(2x^2-x-15) = 3x((2x+5)(x-3)
The expressions for the length, width, and height are [tex]3x, (2x+5)[/tex] and [tex](x-3)[/tex].
Important information:
- Volume of the rectangular prism is [tex]6x^3-3x^2-45x[/tex].
We need to find the expressions for length, width, and height.
Volume of rectangular prism:
The volume of a rectangular prism is the product of its length, width and height.
[tex]V=l\times b\times h[/tex]
We have,
[tex]V=6x^3-3x^2-45x[/tex]
Taking out the common factors.
[tex]V=3x(2x^2-x-15)[/tex]
[tex]V=3x(2x^2-6x+5x-15)[/tex]
[tex]V=3x(2x(x-3)+5(x-3))[/tex]
[tex]V=3x(2x+5)(x-3)[/tex]
Therefore, the expressions for the length, width, and height are [tex]3x, (2x+5)[/tex] and [tex](x-3)[/tex].
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