Given that f, of, x, equals, x, squared, minus, 6, x, minus, 40*f*(*x*)=*x*2−6*x*−40 and g, of, x, equals, x, minus, 10*g*(*x*)=*x*−10, find f, of, x, minus, g, of, x*f*(*x*)−*g*(*x*) and express the result as a polynomial in simplest form

We are given the following two functions:

\[
f(x) = x^2 - 6x - 40
\]
and
\[
g(x) = x - 10
\]

We need to find \( f(x) - g(x) \), and express the result as a polynomial in its simplest form.

### Step 1: Write out the expression for \( f(x) - g(x) \)

\[
f(x) - g(x) = (x^2 - 6x - 40) - (x - 10)
\]

### Step 2: Distribute the negative sign

\[
f(x) - g(x) = x^2 - 6x - 40 - x + 10
\]

### Step 3: Combine like terms

- Combine the \( x \)-terms: \( -6x - x = -7x \)
- Combine the constants: \( -40 + 10 = -30 \)

Thus, we have:

\[
f(x) - g(x) = x^2 - 7x - 30
\]

### Final answer:

\[
f(x) - g(x) = x^2 - 7x - 30
\]

This is the result expressed as a polynomial in its simplest form.

Do you want any details about the process or have any questions?

Here are 5 related questions:
1. What is the degree of the polynomial \( f(x) - g(x) \)?
2. How would you find the roots of the polynomial \( f(x) - g(x) \)?
3. What happens to \( f(x) - g(x) \) when \( x = 5 \)?
4. Can you factor the polynomial \( f(x) - g(x) \)?
5. How would the expression change if \( g(x) \) were \( x + 10 \) instead?

**Tip:** When simplifying expressions, always distribute negative signs carefully to avoid mistakes.

Given that f(x) = x^2 - 6x - 40 and g(x) = x - 10, find f(x) - g(x) and express the result as a polynomial in simplest form.

Learn how to simplify the expression f(x) - g(x) where f(x) = x^2 - 6x - 40 and g(x) = x - 10. This step-by-step guide covers polynomial subtraction, distributing negative signs, and combining like terms, ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation