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 in factored form.


I would like it if you put down all the steps and explanation for I do not understand it. Thank you so much for your help in advance!

Answer 1

Answer:

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

Step-by-step explanation:

f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4

Step 1. Calculate the difference between the functions

(a) Write the two functions, one above the other, in decreasing order of exponents.

ƒ(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³           - 7x + 4

(b) Create a subtraction problem using the two functions

        ƒ(x) =    9x³ + 2x² - 5x + 4

      -g(x) =  -(5x³           - 7x + 4)

ƒ(x) -g(x)=

(c). Subtract terms with the same exponent of x

        ƒ(x)   =    9x³ + 2x² - 5x + 4

      -g(x)  =   -(5x³          -  7x + 4)

ƒ(x) -g(x) =      4x³ + 2x² + 2x

Step 2. Factor the expression

y = 4x³ + 2x² + 2x

Factor 2x from each term

y = 2x(2x² + x + 1)

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