Question

What is (f x g)(x){f(x)=x^3-4x+2g(x)=x^2-6Write your answer in standard form.

Answer 1

`(f* g)(x)=x^5-10x^3+2x^2+24x-12`

STEP - BY - STEP EXPLANATION

What to find?

(f x g)(x)

Given:

`\begin{gathered} f(x)=x^3-4x+2 \\ g(x)=x^2-6 \end{gathered}`

To solve the problem, we will follow the steps below:

Step 1

Express (f x g)(x)

That is;

`(f* g)(x)=f(x)* g(x)`

Step 2

Substitute the function into the above.

`=(x^3-4x+2)(x^2-6)`

Step 3

Open the parenthesis.

`=x^2(x^3-4x+2)-6(x^3-4x+2)`
`=x^5-4x^3+2x^2-6x^3+24x-12`

Step 4

Re-arrange and simplify.

`=x^5-4x^3-6x^3+2x^2+24x-12`
`=x^5-10x^3+2x^2+24x-12`

Therefore,

`(f* g)(x)=x^5-10x^3+2x^2+24x-12`