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 final answer in factored form.

Step-by-step explanation:

f(x) - g(x)

9x³+2x²-5x+4 - (5x³-7x+4)

9x³+2x²-5x+4 - 5x³+7x-4

4x³+2x²+2x

2x(2x²+x+1)

Part a: every term contains a y, so y is a part of the gcf every term contains a factor of 2, and the lowest is 2 so 2y is the gcf factoring out gcf, we get 2y(x³ + 4x - 2x² - 8)    part b: we factor 2y(x³ + 4x - 2x² - 8) by grouping 2y(x³ + 4x - 2x² - 8) = 2y[x(x² + 4) - 2(x² + 4)] = 2y(x-2)(x²+4)