The polynomial 2x^3 + 9x^2 + 4x - 15 represents the volume in cubic feet of a rectangular holding tank at a fish hatchery. The depth of the tank is (x-1) feet. The length is 13 feet. Assume the length is the greatest dimension. Which linear factor represents the 13-ft length? What are the dimensions of the tank?

Question

Mathematics

Natalya Henry

29 July, 08:24

The polynomial 2x^3 + 9x^2 + 4x - 15 represents the volume in cubic feet of a rectangular holding tank at a fish hatchery. The depth of the tank is (x-1) feet. The length is 13 feet. Assume the length is the greatest dimension. Which linear factor represents the 13-ft length? What are the dimensions of the tank?

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Paxton · Answer 1

For part A: you will get 3 linear factors (as the degree of the polynomial is 3). perform the division using (x-1) as your known factor and you will get (x-1) (2x²+11x+15). you can then factor the (2x²+11x+15) to get 2x^3 + 9x^2 + 4x - 15 = (x-1) (2x+5) (x+3)

for part B: since 2x+5 will provide the greatest value (assuming x>0) of the 3 factors, then 2x+5=13. solve to get x=4. if x is 4, then the dimensions are 3'x13'x7' [just sub 4 into the x's for each factor]

for part C: as to the graphing calculator, I don't have one. However, if you solve each linear factor for when it is 0, those values will be the x-intercepts. So your graph should cross the x-asix at 1, - 5/2, and - 3