To solve this problem you must apply the proccedure shown below:
1. You have the following functions given in the problem above:
[tex]f(x)=x-6
[/tex] and [tex]g(x)=x1/2(x+3)=x(x+3)/2 [/tex]
2. You have that g(x) times f(x) can be written as g(x)*f(x). Therefore, you must multiply f(x) * g(x), as following:
[tex]g(x)*f(x)=(x-6)*x(x+3)/2 [/tex]
3. Applying the distributive property, you have:
[tex]g(x)*f(x)=( x^{3} + 3x^2 - 6x^{2} -18x)/2[/tex]
[tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2 [/tex]
The answer is: [tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2[/tex]
