Step-by-step explanation:
The first one (f×g)(x) is asking you what is f of x times g of x. This means you multiply the function. You can multiply by the first term (5x) then the second (3) and combine like terms.
[tex] {15x}^{2} (5x) = {75x}^{3} \\ 19x(5x) = 95 {x}^{2} \\ 6(5x) = 30x[/tex]
[tex] {15x}^{2} (3) = 45 {x}^{2} \\ 19x(3) = 57x \\ 6(3) = 18[/tex]
Combine like terms
[tex] {75x}^{3} + {95x}^{2} + {45x}^{2} + 30x + 57x \\ + 18 = \\ {75x}^{3} + {140x}^{2} + 87x + 18[/tex]
The second one asks you to divide.
Factor out f(x):
[tex] {15x}^{2} + 19x + 6[/tex]
From dividing f(x) /g(x)
[tex] \frac{ {15x}^{2} + 19x + 6 }{5x + 3} [/tex]
To
[tex] \frac{(5x + 3)(3x + 2)}{5x + 3} [/tex]
Cancel like terms since (5x+3) is on top and bottom of fraction.
You get 3x+2
