Question

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.

Answer 1

`(2x+5)(x+3)`

Explanation:

The polynomial
`2x^3 + 9x^2 + 4x - 15` 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

`(2x^3 + 9x^2 + 4x - 15)/(x-1)`

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

`2x^2+11x+15`

product is 2 times 15 = 30

sum is 11

6 times 5 is 30 , 6 plus 5 is 11

`(2x^2+6x)+(5x+15)` , take out GCF from each group

`2x(x+3)+5(x+3)`

`(2x+5)(x+3)`