Question 1131353: The volume of a rectangular box is found by multiplying its length, width, and
height: V = lwh. A certain box has a volume of b³+3b²-4b-12. Factor the four-term
polynomial to find the dimensions of the box.
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
b³+3b²-4b-12
Factor by grouping
Group the first two terms: b³+3b² factors as b²(b+3)
Factor the last two terms: -4b-12 factors as -4(b+3)
So b³+3b²-4b-12 equals b²(b+3)-4(b+3)
Take out the common factor (b+3) and get (b+3)(b²-4)
Factor the second parentheses as the difference of
squares (b-2)(b+2), which means that
b³+3b²-4b-12 equals (b+3)(b-2)(b+2)
Therefore the dimensions are b+3, b-2, and b+2 where b > 2
Since these three factors are the dimensions of a box, they
cannot be negative. So b must be greater than 2 to prevent
b-2 from being negative.
Edwin
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