I need to know the steps to complete this equation please help.
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.
surely you can simplify
9x^3+2x^2-5x+4 - (5x^3-7x+4)
Hint: there will be a common factor of 2x
The other quadratic multiplier does not factor
To find f(x) - g(x), we will subtract every corresponding term of f(x) from the corresponding term of g(x). Here are the steps:
Step 1: Write down the original equation:
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
Step 2: Distribute the subtraction sign to every term in g(x):
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - (5x^3 - 7x + 4)
Step 3: Remove the parentheses by changing the subtraction sign inside to addition and negating the sign of every term inside the parentheses:
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Step 4: Combine like terms:
(9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4)
Step 5: Simplify:
4x^3 + 2x^2 + 2x
The final answer in factored form is:
f(x) - g(x) = 2x(2x^2 + x + 1)