+43 What are the dimensions of a rectangular box with a volume of 50b^3 + 75b^2 - 2b - 3?
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)
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)
+37146 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...
