Answer:  

(2x+3)(3x+4)(3x+5)

Step-by-step explanation:

18x

3

+81x

2

+121x+60−0

By Rational Root Theorem, all rational roots of a polynomial are in the form  

q

p

​

, where p divides the constant term 60 and q divides the leading coefficient 18. One such root is −

3

5

​

. Factor the polynomial by dividing it by 3x+5.

(3x+5)(6x

2

+17x+12)

Consider 6x

2

+17x+12. Factor the expression by grouping. First, the expression needs to be rewritten as 6x

2

+ax+bx+12. To find a and b, set up a system to be solved.

a+b=17

ab=6×12=72

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 72.

1,72

2,36

3,24

4,18

6,12

8,9

Calculate the sum for each pair.

1+72=73

2+36=38

3+24=27

4+18=22

6+12=18

8+9=17

The solution is the pair that gives sum 17.

a=8

b=9

Rewrite 6x

2

+17x+12 as (6x

2

+8x)+(9x+12).

(6x

2

+8x)+(9x+12)

Factor out 2x in the first and 3 in the second group.

2x(3x+4)+3(3x+4)

Factor out common term 3x+4 by using distributive property.

(3x+4)(2x+3)

Rewrite the complete factored expression.

(2x+3)(3x+4)(3x+5)