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What are the dimensions of a rectangular box with a volume of 50b^3 + 75b^2 - 2b - 3?

 Feb 9, 2017

Best Answer 

 #1
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+10

Factor the following:
50 b^3 + 75 b^2 - 2 b - 3

Factor terms by grouping. 50 b^3 + 75 b^2 - 2 b - 3 = (50 b^3 + 75 b^2) + (-3 - 2 b) = 25 b^2 (2 b + 3) - (2 b + 3):
25 b^2 (2 b + 3) - (2 b + 3)

Factor 2 b + 3 from 25 b^2 (2 b + 3) - (2 b + 3):
(2 b + 3) (25 b^2 - 1)

25 b^2 - 1 = (5 b)^2 - 1^2:
(5 b)^2 - 1^2 (2 b + 3)

Factor the difference of two squares. (5 b)^2 - 1^2 = (5 b - 1) (5 b + 1):
Answer: |(5 b - 1)* (5 b + 1)* (2 b + 3)

 Feb 9, 2017
 #1
avatar
+10
Best Answer

Factor the following:
50 b^3 + 75 b^2 - 2 b - 3

Factor terms by grouping. 50 b^3 + 75 b^2 - 2 b - 3 = (50 b^3 + 75 b^2) + (-3 - 2 b) = 25 b^2 (2 b + 3) - (2 b + 3):
25 b^2 (2 b + 3) - (2 b + 3)

Factor 2 b + 3 from 25 b^2 (2 b + 3) - (2 b + 3):
(2 b + 3) (25 b^2 - 1)

25 b^2 - 1 = (5 b)^2 - 1^2:
(5 b)^2 - 1^2 (2 b + 3)

Factor the difference of two squares. (5 b)^2 - 1^2 = (5 b - 1) (5 b + 1):
Answer: |(5 b - 1)* (5 b + 1)* (2 b + 3)

Guest Feb 9, 2017
 #2
avatar+18055 
+5

Thanx Guest 1     .....    I learned from your answer how to do this mathematically.   I typically revert to graphical solutions when I do not know how to calculate an answer...here is the graph of the equation...... you can see the zeros are at -.2 +.2 and -1.5     so the dimensions are

(b+1.5)(b-.2)(b+.2)      which is the same as guest calculated (though simplified)

 

 

 

Well ....  image uploader is not funcioning presently....will post graph when it becomes available...

 Feb 9, 2017

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