Question

given that $f(x) = x^2 - 8x - 20$ and $g(x) = x - 10$, find $f(x) - g(x)$ and express the result as a polynomial in simplest form.

Explanation:

Step1: Substitute the functions

We know \( f(x)=x^{2}-8x - 20 \) and \( g(x)=x - 10 \), so \( f(x)-g(x)=(x^{2}-8x - 20)-(x - 10) \).

Step2: Distribute the negative sign

Distribute the negative sign to each term in \( g(x) \): \( x^{2}-8x - 20 - x+ 10 \).

Step3: Combine like terms

Combine the \( x \)-terms and the constant terms: \( x^{2}+(-8x - x)+(-20 + 10)=x^{2}-9x - 10 \).

Answer:

\( x^{2}-9x - 10 \)