Given that f, of, x, equals, x, squared, plus, 12, x, plus, 20f(x)=x

Question

2
+12x+20 and g, of, x, equals, x, plus, 10g(x)=x+10, find f, of, x, minus, g, of, xf(x)−g(x) and express the result as a polynomial in simplest form.

Answer 1

To find \( f(x) - g(x) \), we first need to write down the functions explicitly:

1. \( f(x) = x^2 + 12x + 20 \)
2. \( g(x) = x + 10 \)

Now, we will subtract \( g(x) \) from \( f(x) \):

\[ f(x) - g(x) = (x^2 + 12x + 20) - (x + 10) \]

Next, we will distribute the subtraction across the terms in \( g(x) \):

\[ f(x) - g(x) = x^2 + 12x + 20 - x - 10 \]

Now, we will combine like terms:

• For the \( x \) terms: \( 12x - x = 11x \)
• For the constant terms: \( 20 - 10 = 10 \)

Thus, we have:

\[ f(x) - g(x) = x^2 + 11x + 10 \]

The final result, expressing \( f(x) - g(x) \) as a polynomial in simplest form, is:

\[ \boxed{x^2 + 11x + 10} \]