Answer:
B
Step-by-step explanation:
We have the two functions:
First, let's factor each of the functions:
Factor out a 2x:
Factor:
Factor our second function:
Factor:
Now, let's see what happens if we add them together. This will yield:
We can rewrite this as:
Using grouping (or the reverse of our distribute property), we can write this as:
However, we want our function to be divisible by (2x+3). We have (2x+1).
So, we can multiply our g(x) by 3. If will go back, this will yield:
Now, we can do grouping again:
Since this now has a (2x+3) term, this is divisible by (2x+3).
So, the equation that is divisible by (2x+3) is f(x)+3g(x).
Our answer is B.
And we're done!