Question

The functions f(x)=√x^2+12x+36 and g(x)=x^3-12 are defined below. Which expression is equal to f(x) · g(x)? A.x^4-6x^3-12x+72 B.x^4-12x^3+6x-72 C.x^4+6x^3-12x-72 D. 7x^3-12x-72

Answer 1

C: x^4+6x^3-12x-72

Explanation:

For the function : f(x)=√x^2+12x+36

It can be factorized to

f(x)=√(x+6)²

=x+6

f(x)*g(x)

=(x+6)(x^3-12)

Expand the brackets

=x^4-12x+6x^3-72

rearrange the numbers

x^4+6x^3-12x-72