F m (x) = x2 + 3 and n (x) = 5x + 9, which expression is equivalent to (mn) (x) ?

A. 5x3 + 9x2 + 15x + 27

B. 25x2 + 90x + 84

C. x2 + 5x + 12

D. 5x2 + 24

m (x) = x² + 3 and n (x) = 5x + 9

By multiplying the two functions∴ (mn) (x) = (x² + 3) (5x+9)

= x² (5x+9) + 3 (5x+9)

= 5x³ + 9x² + 15x + 27

The correct answer is option A / /

A. 5x3 + 9x2 + 15x + 27

To find mn (x), we multiply the given functions m (x) and n (x), to get (x^2 + 3) (5x + 9) = 5x^3 + 9x^2 + 15x + 27. No further simplification is necessary.

This is choice A. Note that by inspection, it can be seen that m (x) * n (x) should result in a cubic expression, and only A has a cubic term 5x^3, while the rest only have up to quadratic (x^2) terms.