Given:

Given: f(x) = g(x) = x²-3x-28 x²-8x+16 x²- 5x + 4 x²-49

Multiplication and Division of Function *

23-25.)

(fg)(x)

26-28.) ()()

It seems like you have a list of functions and operations, but the formatting is a bit unclear. Let me clarify what you're asking. You seem to have several functions involving polynomials, and you want to perform operations like multiplication and division on these functions.

### Clarifying the Problem

Given functions:
- \( f(x) = g(x) = x^2 - 3x - 28 \)
- Another expression might be \( x^2 - 8x + 16 \), \( x^2 - 5x + 4 \), and \( x^2 - 49 \), but their relationship to \( f(x) \) and \( g(x) \) is not clear. I’ll assume they are separate functions, so let’s denote them as:
  - \( h(x) = x^2 - 8x + 16 \)
  - \( k(x) = x^2 - 5x + 4 \)
  - \( m(x) = x^2 - 49 \)

Now, you need to:
1. Find the product \( (fg)(x) \).
2. Determine other operations, possibly products or compositions of other functions like \( (hk)(x) \) or \( (hm)(x) \).

### 1. Multiply the functions \( f(x) \) and \( g(x) \):

Since \( f(x) = g(x) = x^2 - 3x - 28 \), the product \( (fg)(x) \) would be:

\[
(fg)(x) = (x^2 - 3x - 28) \cdot (x^2 - 3x - 28)
\]

This requires expanding the expression:

\[
(fg)(x) = (x^2 - 3x - 28)^2
\]

Expanding this using the distributive property (or by recognizing it as a binomial squared):

\[
(fg)(x) = (x^2 - 3x - 28)(x^2 - 3x - 28)
\]

Now expand:

\[
= x^4 - 6x^3 + 9x^2 - 56x^2 + 168x + 784
\]

Combine like terms:

\[
(fg)(x) = x^4 - 6x^3 - 47x^2 + 168x + 784
\]

### 2. Perform other operations

If you have to perform other operations, please provide the exact operations you need (like division or composition), and specify which functions to use.

Do you want any details or have questions on these calculations?  
Here are five related questions:

1. How do you factor the polynomial \( x^2 - 3x - 28 \)?
2. What is the general formula for multiplying two quadratic functions?
3. How do you find the roots of the polynomial \( x^4 - 6x^3 - 47x^2 + 168x + 784 \)?
4. Can you perform division of the polynomials \( f(x) \) and \( h(x) \)?
5. How do you check if the expanded form of a polynomial is correct?

**Tip:** When multiplying polynomials, carefully expand and combine like terms to ensure accuracy in your final expression.

Given: f(x) = g(x) = x² - 3x - 28, x² - 8x + 16, x² - 5x + 4, x² - 49. Multiplication and Division of Function. (fg)(x)

Explore the multiplication of polynomial functions using the given functions f(x) = g(x) = x² - 3x - 28. Learn how to expand and simplify the product (fg)(x), and understand the key algebraic concepts involved. Suitable for Grades 9-11 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation