Question

Which expression is equal to f(x) · g(x)?

Answer 1

C. x⁴ + 6·x³ - 12·x - 72

Step-by-step explanation:

The given functions are;

`f(x) =√(x^2 + 12 \cdot x + 36)`

g(x) = x³ -12

We have that
`f(x) =√(x^2 + 12 \cdot x + 36)` =
`f(x) =√((x + 6)^2)` = (x + 6)

Therefore;

f(x)·g(x) =
`√(x^2 + 12 \cdot x + 36)` × (x³ - 12) = (x + 6) × (x³ - 12)

(x + 6) × (x³ - 12) = x⁴ - 12·x + 6·x³ - 72 = x⁴ + 6·x³ - 12·x - 72

∴ f(x)·g(x) =
`√(x^2 + 12 \cdot x + 36)` × (x³ - 12) = x⁴ + 6·x³ - 12·x - 72