The polynomial 2x3 + 9x2 + 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.

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lisboa lisboa · Answer 1 · 2020-01-08T06:14:34+01:00

Answer:

[tex](2x+5)(x+3)[/tex]

Step-by-step explanation:

The polynomial [tex]2x^3 + 9x^2 + 4x - 15[/tex] represents the volume in cubic feet of a rectangular holding tank at a fish hatchery

Use synthetic division to find the expressions representing the other sides of the tank

[tex]\frac{2x^3 + 9x^2 + 4x - 15}{x-1}[/tex]

x-1=0 , add 1 on both sides

x=1, write all the coefficients and then divide by 1

In synthetic division, drop the first number

then multiply it with 1 and write it below the second number.

Add it and do the same

1 2 9 4 -15

0 2 11 15

-------------------------------------

2 11 15 0

Remainder is 0

Frame expression using the numbers 2 11 and 15

[tex]2x^2+11x+15[/tex]

product is 2 times 15 = 30

sum is 11

6 times 5 is 30 , 6 plus 5 is 11

[tex](2x^2+6x)+(5x+15)[/tex] , take out GCF from each group

[tex]2x(x+3)+5(x+3)[/tex]

[tex](2x+5)(x+3)[/tex]