Given that f, of, x, equals, x, squared, minus, 11, x, plus, 30f(x)=x
2
−11x+30 and g, of, x, equals, x, minus, 5g(x)=x−5, find left parenthesis, f, minus, g, right parenthesis, left parenthesis, x, right parenthesis(f−g)(x) and express the result as a polynomial in simplest form.
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We are asked to find \( (f - g)(x) \), which means we need to subtract the function \( g(x) \) from \( f(x) \).

Given:
\[
f(x) = x^2 - 11x + 30
\]
\[
g(x) = x - 5
\]

Now, let's compute \( (f - g)(x) \):
\[
(f - g)(x) = f(x) - g(x)
\]
Substitute \( f(x) \) and \( g(x) \):
\[
(f - g)(x) = (x^2 - 11x + 30) - (x - 5)
\]

Distribute the negative sign:
\[
(f - g)(x) = x^2 - 11x + 30 - x + 5
\]

Now, combine like terms:
\[
(f - g)(x) = x^2 - 12x + 35
\]

Thus, the result is:
\[
(f - g)(x) = x^2 - 12x + 35
\]

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. What is the result of adding \( f(x) \) and \( g(x) \) instead of subtracting?
2. How can we find the product of \( f(x) \) and \( g(x) \)?
3. How do you find the roots of the polynomial \( f(x) \)?
4. What is the graphical interpretation of subtracting two functions?
5. How do you find the vertex of the quadratic function \( f(x) = x^2 - 12x + 35 \)?

**Tip:** When subtracting functions, always distribute the negative sign carefully to avoid mistakes with signs in each term.

Given that f(x) = x^2 - 11x + 30 and g(x) = x - 5, find (f - g)(x) and express the result as a polynomial in simplest form.

Learn how to subtract two functions, f(x) = x^2 - 11x + 30 and g(x) = x - 5, and express the result as a simplified polynomial. This problem covers key algebraic concepts such as polynomial subtraction and function operations. Ideal for students in Grades 9-11.

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