Question

If 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

Answer 1

`5x^3 +9x^2 +15x+27`

Explanation:

If m(x) = x2 + 3 and n(x) = 5x + 9,

(mn)(x) is (m times n)(x)= m(x) times n(x)

m(x) * n(x)

Plug in m(x) and n(x). then multiply it

m(x) * n(x)

(x^2 + 3)(5x+9)

Apply FOIL method to multiply it

x^2 * 5x = 5x^3

x^2 * 9 = 9x^2

3*5x= 15x

3*9 = 27

`5x^3 +9x^2 +15x+27`

Answer 2

Answer: A

Explanation:

m(x) = x² + 2

n(x) = 5x + 9

(m*n)(x) = (x² + 3)(5x + 9)

= x²(5x + 9) + 3(5x + 9)

= 5x³ + 9x² + 15x + 27