Respuesta :
The expression for the rectangular prism's base area is 11x² + 7x + 5.
Given;
The volume of rectangular prism = 33x³ + 43x² + 29x + 10
The height of the prism = 3x + 2
We know that, the area of the prism = length * breadth
where as, volume = length * breadth * height
So, area = volume / height
Using synthetic division, dividing volume by height, we get;
3x+2 ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5
33x3 + 22x2
---------------------------------
21x² + 29x
21x² + 14x
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15x + 10
15x + 10
----------------------------------
x
Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.
To learn more about synthetic division click here:
brainly.com/question/28824872
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