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marshall27 [118]

3 years ago

latex-formula">
F(x)15x^2+19x+6 and g(x)=5x+3

Mathematics

1 answer:

navik [9.2K]3 years ago

4 0

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

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