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.
just do a direct substitution.
f(x)-g(x) = (9x^3 + 2x^2 − 5x + 4) - (5x^3 −7x + 4)
= 9x^3 + 2x^2 − 5x + 4 - 5x^3 + 7x - 4
= (9-5)x^3 + (2+0)x^2 + (-5+7)x + (4-4)
= 4x^3 + 2x^2 + 2x
= 2x(2x^2+x+1)
To find f(x) - g(x), we need to subtract the two functions term by term.
Given:
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
Step 1: Subtract the coefficients of the same degree terms.
Subtract the coefficients of the x^3 terms:
9x^3 - 5x^3 = (9 - 5)x^3 = 4x^3
Subtract the coefficients of the x^2 terms:
2x^2 - 0 = 2x^2
Subtract the coefficients of the x terms:
-5x - (-7x) = -5x + 7x = 2x
Subtract the constant terms:
4 - 4 = 0
Step 2: Combine the terms to express the difference in factored form.
f(x) - g(x) = 4x^3 + 2x^2 + 2x + 0
Simplifying, the final answer is:
f(x) - g(x) = 4x^3 + 2x^2 + 2x
Therefore, the difference of f(x) - g(x) in factored form is 4x^3 + 2x^2 + 2x.