Question

the volume of a rectangular solid, in cubic inches, is given by the expression (x^3-7x+6). if the length and width in inches, are given by the expressions (x-2) and (x+3) respectively, find an expression in x which describes the height.

Answer 1

V=x³-7x+6, V=(x-2)(x+3)*h

(x-2)(x+3)*h=x³-7x+6

h{x²+x-6}=x³-7x+6

h=(x³-7x+6)/(x²+x-6)

Therefore h=x-1

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Check answer:

V=(x-2)(x+3)(x-1)

=(x-1)(x²+x-6)

=x(x²+x-6)-1(x²+x-6)

=x³+x²-6x-x²-x+6

=x³-6x-x+6

=x³-7x+6