Answer:
[tex]B=3[/tex]
Step-by-step explanation:
We have been given an expression [tex]12x^4+30x^3+4x^2+10x[/tex].
Let us factor our given expression to answer the given problem.
Factor out [tex]2x[/tex] from all terms:
[tex]2x(6x^3+15x^2+2x+5)[/tex]
Now, we will make two groups of [tex]6x^3+15x^2+2x+5[/tex] as shown below:
[tex]2x((6x^3+15x^2)+(2x+5))[/tex]
[tex]2x((6x^3+15x^2)+(2x+5))[/tex]
Factor out [tex]3x^2[/tex] from 1st group:
[tex]2x((3x^2(2x+5))+(2x+5))[/tex]
[tex]2x(3x^2+1)(2x+5)[/tex]
Upon comparing [tex]2x(3x^2+1)(2x+5)[/tex] with [tex]Ax(Bx^2+1)(2x+5)[/tex], we can see that [tex]A=2[/tex] and [tex]B=3[/tex].
Therefore, the value of B is 3.
