The volume of a rectangular solid is given by the polynomial #8x^4-8x^3-24x^2-3400x# The length of the solid is given by #8x# and the width is given by #x - 5#. Find the height of the solid?

1 Answer
P dilip_k
Apr 8, 2017

The volume of a rectangular solid is given by the polynomial

#8x^4-8x^3-24x^2-3400x#

-The length of the solid is given by #8x# and the width is given by #x - 5#. so the polynomial will have factors #8x# and #x - 5# . Factorizing we get

#8x^4-8x^3-24x^2-3400x#

#=8x(x^3-x^2-3x-425)#

#=8x(x^3-5x^2+4x^2-20x+17x-425)#

#=8x{x^2(x-5)+4x(x-5)+17(x-25)}#

#=8x(x-5)(x^2+4x+17)#

#="length"xx"width"xxheight"#

So height of the polynomial is #(x^2+4x+17)#

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