Answer: the second option is the correct answer.
Step-by-step explanation:
f(x) = 15x² + 19x + 6
g(x) = 5x + 3
f.g(x) = (15x² + 19x + 6)(5x + 3)
f.g(x) = 75x³ + 95x² + 30x + 45x² + 57x + 18
f.g(x) = 75x³ + 95x² + 45x²+ 30x + 57x + 18
f.g(x) = 75x³ + 140x²+ 87x + 18
(f ÷ g)(x) = (15x² + 19x + 6)/(5x + 3)
We would find the other factor of the quadratic equation.
15x² + 19x + 6 = 0
We would find two numbers such that their sum or difference is 19x and their product is 90x². The two numbers are 10x and 9x. Therefore,.
15x² + 10x + 9x + 6 = 0
5x(3x + 2) + 3(3x + 2)
(3x + 2)(5x + 3)
Therefore,
(f ÷ g)(x) = 3x + 2
