If m(x) = x² + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?
5x³ + 9x² + 15x + 27
25x² + 90x + 84
x² + 5x + 12
5x² + 24

Solution:

It is given that

m(x) = x² + 3

n(x) = 5x + 9

We have to find the expression which is equivalent to (mn) (x)

Substituting the values we get

(mn) (x) = (x² + 3) (5x + 9)

Using the distributive property of multiplication

(mn) (x) = x² (5x + 9) + 3 (5x + 9)

So we get

(mn) (x) = 5x³ + 9x² + 15x + 27

Therefore, the expression which is equivalent to (mn) (x) is 5x³ + 9x² + 15x + 27.

If m(x) = x² + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?
5x³ + 9x² + 15x + 27
25x² + 90x + 84
x² + 5x + 12
5x² + 24

Summary:

If m(x) = x² + 3 and n(x) = 5x + 9, the expression which is equivalent to (mn) (x) is 5x³ + 9x² + 15x + 27.