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

ANSWER

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

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;

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