f(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4. what is f(x)-g(x). Show all your steps and write you final answer in factored form.
3 points
subtract the like (same order) terms
(9x^3 - 5x^3) + 2x^2 - (5x -7x) + (4 - 4) ... 4x^3 + 2x^2 + 2x ... 2x (2x^2 + x + 1)
F(x)-g(x) = (9x^3 + 2x^2 -5x + 4) - (5x^3 - 7x + 4).
F(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4 = 4x^3 + 2x^2 + 2x = 2x(2x^2 + x + 1).
To find f(x) - g(x), we need to subtract g(x) from f(x) by subtracting the corresponding coefficients of the same degree terms.
Given:
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
Step 1: Write the subtraction expression
f(x) - g(x) = (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
Step 2: Distribute the negative sign
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Step 3: Combine like terms
f(x) - g(x) = (9x^3 - 5x^3) + 2x^2 + (-5x + 7x) + (4 - 4)
Step 4: Simplify each part
f(x) - g(x) = 4x^3 + 2x^2 + 2x + 0
The final answer in factored form is:
f(x) - g(x) = 2x(2x^2 + x + 1) + 0
Therefore, f(x) - g(x) = 2x(2x^2 + x + 1).