Given that f, of, x, equals, x, squared, plus, 14, x, plus, 45f(x)=x

Question

Given that f, of, x, equals, x, squared, plus, 14, x, plus, 45f(x)=x 
2
 +14x+45 and g, of, x, equals, x, plus, 5g(x)=x+5, find f, of, x, plus, g, of, xf(x)+g(x) and express the result as a polynomial in simplest form.

GPT-4o mini · Answer

To find $ f(x) + g(x) $ for the given functions $ f(x) = x^2 + 14x + 45 $ and $ g(x) = x + 5 $, we will first compute $ f(x) $ and $ g(x) $ individually and then add them together. 1. We have: $$ f(x) = x^2 + 14x + 45 $$ $$ g(x) = x + 5 $$ 2. Now, we add $ f(x) $ and $ g(x) $: $$ f(x) + g(x) = (x^2 + 14x + 45) + (x + 5) $$ 3. Combine like terms: $$ f(x) + g(x) = x^2 + 14x + x + 45 + 5 $$ 4. Simplifying further: $$ f(x) + g(x) = x^2 + 15x + 50 $$ Thus, the result $ f(x) + g(x) $ expressed as a polynomial in simplest form is: $$ \boxed{x^2 + 15x + 50} $$