A rectangle has a length of 10 units and a width of 8 units. Squares of x by x units are cut out of each corner, and then.. For the following exercises, write the polynomial function that models the given situation.

For the following exercises, write the polynomial function that models the given situation.

A rectangle has a length of 10 units and a width of 8 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x.

Solutions

Expert Solution

Consider the following for an open box,

l = 10 – 2x

w = 8 – 2x

h = x

Consider the formula for volume of the open box,

v = l × w × h

Put the values in the formula,

v = l × w × h

= (10 – 2x)(8 – 2x)x

v = 2x(5 – x)(4 – x)

= 2x(20 – 5x – 4x + x2)

= 2x3 – 18x2 + 40x

Hence, the polynomial is v = 2x3 – 18x2 + 40x.

Junaid answered 9 months ago

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