Part

c. the volume of a rectangular box is (x3 - 7x2 - 9x + 63) cubic units. determine the dimensions of the rectangular box by factoring the volume expression completely. show your work.

The last term is 63 so 3 might be a zero of the function; -

f (3) = 27 - 7*9 - 3*9 + 63 = 27 - 63 - 27 + 63 = 0 so 3 is a zero and

therefore (x - 3) is a factor of the volume function.

Long division of the expression by x - 3 gives the quotient:-

x^2 + 4x - 21

Factoring this:-

= (x + 7) (x - 3)

So the dimensions of the box are, x-3, x-3 and x+7 answer.