Respuesta :
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]
