Question

Enter your answer and show all the steps that you use to solve this problem in the space provided. f(x)=9x^3+2x^2-5x+4 And g(x)=5x^3-7x+4. What is f(x)-g(x)? Show all of your steps and write your final answer I’m factored form.

Can anyone help me? Thank you:)

Answer 1

`f(x) - g(x) =2x(2 {x}^(2) + x + 1)`

Step-by-step explanation

The given polynomials are;

`f(x) =9{x}^(3) + 2 {x}^(2) - 5x + 4`

and

`g(x) = 5 {x}^(3) - 7x + 4`

`f(x) - g(x) =9{x}^(3) + 2 {x}^(2) - 5x + 4 - (5 {x}^(3) - 7x + 4)`

Expand:

`f(x) - g(x) =9{x}^(3) + 2 {x}^(2) - 5x + 4 - 5 {x}^(3) + 7x - 4`

Regroup similar terms:

`f(x) - g(x) =9{x}^(3) - 5 {x}^(3)+ 2 {x}^(2) - 5x + 7x + 4- 4`

Simplify:

`f(x) - g(x) =4{x}^(3)+ 2 {x}^(2) + 2x`

Factor 2x;

`f(x) - g(x) =2x(2 {x}^(2) + x + 1)`