What are the possible expressions for the dim | vedclass

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(A) The volume of a cuboid is given by the product of its dimensions: $V = 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height}$.Given $V = 2x^3 +

Vedclass · Accepted Answer

$(2x + 5), (x + 4), (x + 1)$

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(A) The volume of a cuboid is given by the product of its dimensions: $V = 	ext{length} 	imes 	ext{breadth} 	imes 	ext{height}$.Given $V = 2x^3 + 15x^2 + 33x + 20$.To find the dimensions, we factorize the polynomial.Let $p(x) = 2x^3 + 15x^2 + 33x + 20$.By testing values, if $x = -1$, $p(-1) = 2(-1)^3 + 15(-1)^2 + 33(-1) + 20 = -2 + 15 - 33 + 20 = 0$.Thus, $(x + 1)$ is a factor.Dividing $2x^3 + 15x^2 + 33x + 20$ by $(x + 1)$ using synthetic division or long division gives $2x^2 + 13x + 20$.Now, factorize the quadratic $2x^2 + 13x + 20$:$2x^2 + 8x + 5x + 20 = 2x(x + 4) + 5(x + 4) = (2x + 5)(x + 4)$.Therefore, the dimensions are $(2x + 5), (x + 4), (x + 1)$.

What are the possible expressions for the dimensions of a cuboid whose volume is given as $(2x^3 + 15x^2 + 33x + 20)$ cubic units? $(x > 0)$

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