The volume of a right rectangular prism is expressed by V(x) = x^3+2x^2-x-2. What could the dimensions of the prism be?

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Answer 1 · 2015-07-11T17:41:35

$V (x) = x^{3} + 2 x^{2} - x - 2 = (x - 1) (x + 1) (x + 2)$ $V(x) = x^3+2x^2-x-2 = (x-1)(x+1)(x+2)$

So the dimensions could be $(x - 1) \times (x + 1) \times (x + 2)$ $(x-1) xx (x+1) xx (x+2)$

Factor by grouping

$V (x) = x^{3} + 2 x^{2} - x - 2$ $V(x) = x^3+2x^2-x-2$

$= (x^{3} + 2 x^{2}) - (x + 2)$ $= (x^3+2x^2)-(x+2)$

$= x^{2} \cdot (x + 2) - 1 \cdot (x + 2)$ $= x^2*(x+2)-1*(x+2)$

$= (x^{2} - 1) (x + 2)$ $= (x^2-1)(x+2)$

$= (x^{2} - 1^{2}) (x + 2)$ $= (x^2-1^2)(x+2)$

$= (x - 1) (x + 1) (x + 2)$ $= (x-1)(x+1)(x+2)$

...using the difference of squares identity:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$