g(x) = x^3 - 2x^2 + 3 and h(x) = x + 1, find the function ( h x g) (x) 

To find \((h \times g)(x)\), you multiply the functions \(g(x)\) and \(h(x)\) together.

Given:
\[
g(x) = x^3 - 2x^2 + 3
\]
\[
h(x) = x + 1
\]

The product of the functions is:
\[
(h \times g)(x) = h(x) \times g(x)
\]

Now, substitute the given functions:
\[
(h \times g)(x) = (x + 1) \times (x^3 - 2x^2 + 3)
\]

Expand this expression by distributing:
\[
(h \times g)(x) = x \times (x^3 - 2x^2 + 3) + 1 \times (x^3 - 2x^2 + 3)
\]

Simplify each term:
\[
(h \times g)(x) = x^4 - 2x^3 + 3x + x^3 - 2x^2 + 3
\]

Now, combine like terms:
\[
(h \times g)(x) = x^4 - x^3 - 2x^2 + 3x + 3
\]

So, the final answer is:
\[
(h \times g)(x) = x^4 - x^3 - 2x^2 + 3x + 3
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the sum of \(g(x)\) and \(h(x)\)?
2. What is the process for finding the difference of \(g(x)\) and \(h(x)\)?
3. How do you find the quotient of \(g(x)\) and \(h(x)\)?
4. What happens when you compose \(g(x)\) and \(h(x)\) to find \((g \circ h)(x)\)?
5. How would you differentiate \((h \times g)(x)\) with respect to \(x\)?

**Tip:** Always carefully combine like terms after expanding polynomials to avoid mistakes in the final expression.

Learn how to calculate (h x g)(x) using the functions g(x) = x^3 - 2x^2 + 3 and h(x) = x + 1. Follow a detailed step-by-step solution including polynomial multiplication, expansion of polynomials, and combining like terms. Suitable for high school 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