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Question

The volume in cubic feet of a box can be expressed as #(x)=x^3-6x^2+8x# , or as the product of three linear factors with integer coefficients. The width of the box is #x-2#.

Factor the polynomial to find linear expressions for the height and the length. Show your work.

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Answer 1 · 2017-09-14T17:38:10

see below

#Vol=x^3-6x+8x#

To express a three linear factors we start the process by looking for common factors in all three terms.

We note that #x# is a common factor

#Vol=x(x^2-6+8x)#

The bracket is a quadratic which will factorise into two brackets

#Vol=x(x-2)(x-4)#

width is given as #(x-2)#

The length is the longest side #x#

leaving #x-4# as the height