Question

PLEASE HELP

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

Answer 1

= 2x²( 2x+ 1) + 2x

or

= 2x (2x² + x + 1)

Explanation:

Given in the question two functions,

f ( x ) = 9x³ + 2x² − 5x + 4

g ( x ) = 5x³ − 7 x + 4

To find,

f ( x ) − g ( x )

Substitute each functions

​= 9x³ + 2x² − 5x + 4 - ( 5x³ − 7 x + 4 )

Remove parentheses ​

= 9x³ + 2x² − 5x + 4 - 5x³ + 7 x - 4

Combine like terms and add them up

= 4x³ + 2x² + 2x

Factorise

= 2x²( 2x+ 1) + 2x

or

= 2x (2x² + x + 1)

So the final answer in factored form is 2x²( 2x+ 1) + 2x or 2x (2x² + x + 1)

This can't be further factorise because answer will be in complex numbers