Polynomial help please

The polynomial x^3 + 3x^2 + 4x +2 is denoted by f(x).
(i) Find the quotient and remainder when f(x) is divided by x^2 + x -1
(ii) Use the factor theorem to show that ( x + 1) is a factor of f(x)



Can you please show full working especially for part (i).

Writing out polynomial division is not easy. Be patient with me.

I set up the long division and look for what will make first term in the divisor work for the term in the dividend. Then I multiply it out and subtract. I bring down the terms from the dividend, and repeat the process.

____________x_+_ 2
x^2 + x - 1| x^3 + 3x^2 + 4x + 2
- (x^3 + x^2 - x)
2x^2 + 5x + 2
- (2x^2 + 2x -2)
3x + 4

Quotient is x + 2 with a remainder of 3x + 4

______x^2_+2x_+2
x + 1| x^3 + 3x^2 + 4x + 2
- (x^3 + x^2)
2x^2 + 4x
- (2x^2 + 2x)
2x + 2
- (2x + 2)
0

Since there is not remainder, (x - 1) is a factor of x^3 + 3x^3 + 4x + 2

All the extra spaces I put into so that terms lines up in columns arre removed. I do not know how to deal with that. This is confusing.
Write it out on a sheet of paper, with the divisor outside of the long division box, and the dividend on the inside.
Then try to process as described at the beginning at refer to the values that I used.
I am sorry I couldn't make it line up in columns. It would make more sense

I can help you with 2. Simply imput -1 into the equation. If it is a factor, the equation will equal 0.
This is the remainder theorm, to find the remainder of a polynomial when it is divided by x+or- and number, imput the opposite of the number in the bracket into the function. I.E F(x)/(x+2), input -2 into f(x) and your remainder is the value you have left :)

x + 1 = 0 means x = -1

x + 1 is a factor of f(x) if f(-1) = 0. Try it, replace x by -1 and compute.

yes