A box in the shape of a rectangular prism has a volume of $6 x^{3} + 27 x^{2} - 15 x$ $6x^3+27x^2-15x$ . What are the dimensions of the box?

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A box in the shape of a rectangular prism has a volume of $6 x^{3} + 27 x^{2} - 15 x$ $6x^3+27x^2-15x$ . What are the dimensions of the box?

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Answer 1 · 2018-05-09T03:44:24

The box measures $3 x$ $3x$ by $2 x - 1$ $2x- 1$ by $x + 5$ $x + 5$ .

Explanation:

We can immediately factor out a $3 x$ $3x$ .

$3 x (2 x^{2} + 9 x - 5)$ $3x(2x^2 + 9x - 5)$

Let's try and factor the trinomial now.

$3 x (2 x^{2} + 10 x - x - 5)$ $3x(2x^2 + 10x - x - 5)$

$3 x (2 x (x + 5) - (x + 5))$ $3x(2x(x + 5) - (x + 5))$

$3 x (2 x - 1) (x + 5)$ $3x(2x - 1)(x + 5)$

Therefore, the box measures $3 x$ $3x$ by $2 x - 1$ $2x- 1$ by $x + 5$ $x + 5$ .

Hopefully this helps!

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A box in the shape of a rectangular prism has a volume of $6 x^{3} + 27 x^{2} - 15 x$ $6x^3+27x^2-15x$ . What are the dimensions of the box?

1 Answer

Explanation:

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A box in the shape of a rectangular prism has a volume of 6x^3+27x^2-15x6x3+27x2−15x6x^3+27x^2-15x. What are the dimensions of the box?

1 Answer

Explanation:

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A box in the shape of a rectangular prism has a volume of $6 x^{3} + 27 x^{2} - 15 x$ $6x^3+27x^2-15x$ . What are the dimensions of the box?