Question

F left parenthesis x right parenthesis equals 9 x cubed plus 2 x squared minus 5 x plus 4 and g left parenthesis x right parenthesis equals 5 x cubed minus 7 x plus 4. what is f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis? show all of your steps and write your final answer in factored form.

Answer 1

The answer is 2x(2x²+x+1).

When we subtract polynomials we combine like terms:
(9x³+2x²-5x+4)-(5x³-7x+4)

9x³-5x³=4x³
2x²- 0 = 2x²
-5x--7x=-5x+7x=2x
4-4=0

This gives us 
4x³+2x²+2x

Each of these is divisible by 2, and each has an x, so we factor those out:
2x(                        )

4x³/2x = 2x²:
2x(2x²                   )

2x²/2x=x:
2x(2x²+x               )

2x/2x = 1:
2x(2x²+x+1)