Given f(x)= x²+5x+6  and h(x) = x+2 and find the folowing  (f-h)(x)

To find \((f-h)(x)\), we need to subtract \(h(x)\) from \(f(x)\):

Given:
\[
f(x) = x^2 + 5x + 6
\]
\[
h(x) = x + 2
\]

Now, compute \((f-h)(x)\):

\[
(f-h)(x) = f(x) - h(x)
\]
\[
(f-h)(x) = (x^2 + 5x + 6) - (x + 2)
\]

Distribute the subtraction:
\[
(f-h)(x) = x^2 + 5x + 6 - x - 2
\]

Combine like terms:
\[
(f-h)(x) = x^2 + 4x + 4
\]

So, \((f-h)(x) = x^2 + 4x + 4\).

Would you like any more details or have any questions?

Here are 5 related questions:
1. How do you find \((f \cdot h)(x)\) given the same functions?
2. What is the result of \((f + h)(x)\) for these functions?
3. How do you find \((f/h)(x)\) and what are the conditions for it to be defined?
4. What is the vertex of the quadratic function \((f-h)(x)\)?
5. How do you find the roots of the equation \((f-h)(x) = 0\)?

**Tip:** When subtracting polynomials, remember to distribute the negative sign to each term in the polynomial you are subtracting.

Given f(x)= x²+5x+6 and h(x) = x+2, find (f-h)(x).

Learn how to subtract polynomial functions with a step-by-step guide on finding (f-h)(x) for the given functions f(x) = x² + 5x + 6 and h(x) = x + 2. Suitable for students in Grades 8-10, this problem covers key algebraic concepts and provides clear explanations.

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