Question

Select the correct answer.

Consider functions f and g.
f(x) = x² + 12x + 36
g(x) = 13-12
.
Which expression is equal to f(x) · g(x),

Answer 1

`\sf B)\ f(x) \cdot g(x) = x^4 + 6x^3 - 12x - 76`

Explanation:

Given functions:

`\sf f(x) = √(x^2+12x+36)\\`

`\sf g(x) = x^3 - 12`

`\sf f(x) \cdot g(x) = \left(√(x^2+12x+36)\right)* (x^3 - 12) \\\\\ \textsf{[rewrite the radicand using the perfect square trinomial rule: $a^2+2ab+b=(a+b)^2$]}\\\\`

`\sf f(x) * g(x) = \left(√((x+6)^2)\right) * \left(x^3 - 12\right)\textsf{[take the square root of the perfect square trinomial]}\\\\\sf f(x) \cdot g(x) = \left(x+6}\right) * \left(x^3 - 12\right) \textsf{[multiply]}\\\\f(x) \cdot g(x) = x\left(x^3 - 12\right) + 6 \left(x^3 - 12\right) \textsf{[simplify]}\\\\f(x) \cdot g(x) = x^4 - 12x + 6x^3 - 76 \textsf{ [rewrite in descending order]}\\\\f(x) \cdot g(x) = x^4 + 6x^3 - 12x - 76`