Question

let $f(x)=2x + 5$ and $g(x)=x^2 - 5x + 4$. perform the function operation and then find the domain.
$f(x)\cdot g(x)$
$f(x)\cdot g(x)=\square$ (simplify your answer.)

Explanation:

Step1: Substitute given functions

$f(x) \cdot g(x) = (2x+5)(x^2-5x+4)$

Step2: Distribute $2x$ to each term

$2x(x^2-5x+4) = 2x^3 -10x^2 +8x$

Step3: Distribute $5$ to each term

$5(x^2-5x+4) = 5x^2 -25x +20$

Step4: Combine like terms

$2x^3 -10x^2 +8x +5x^2 -25x +20 = 2x^3 -5x^2 -17x +20$

Step5: Find domain of polynomial

Polynomials are defined for all real numbers.

Answer:

$f(x) \cdot g(x) = 2x^3 -5x^2 -17x +20$
Domain: All real numbers, or $(-\infty, \infty)$