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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?

Respuesta :

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 
lhmarianateixeira

In this exercise we have to use the knowledge of polynomials to calculate the linear factor to represent a size, in this way we find that:

A) [tex](x-1)(2x+5)(x+3) [/tex]
B) [tex]3X13X7[/tex]
C) 1, -5/2 and -3.

A) If we have a linear factor equal to 3 we will describe the equation as:

[tex](x-1)(2x^2+11x+15)\\ 2x^3 + 9x^2 + 4x - 15 = (x-1)(2x+5)(x+3) [/tex]

B) Since 2x+5 will provide the greatest value (assuming x>0) of the 3 factors, then:

[tex] 2x+5=13\\ x=4\\ 3X13X7[/tex]

C) So your graph should cross the x-asix at 1, -5/2, and -3 .

See more about polynomials at brainly.com/question/17822016

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