Answer:
C. x⁴ + 6·x³ - 12·x - 72
Explanation:
The given functions are;
[tex]f(x) =\sqrt{x^2 + 12 \cdot x + 36}[/tex]
g(x) = x³ -12
We have that [tex]f(x) =\sqrt{x^2 + 12 \cdot x + 36}[/tex] = [tex]f(x) =\sqrt{(x + 6)^2}[/tex] = (x + 6)
Therefore;
f(x)·g(x) = [tex]\sqrt{x^2 + 12 \cdot x + 36}[/tex] × (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) = [tex]\sqrt{x^2 + 12 \cdot x + 36}[/tex] × (x³ - 12) = x⁴ + 6·x³ - 12·x - 72
