Question

Look at picture please worth 15 points please helpppp

Answer 1

3x - y +
`(- 5x^2y)/(3x^3 + 2x^2y - xy^2)`

Explanation:

Hooboy okay here we go.

1.) Rewrite the equation in the classic division method

3x³ + 2x²y - xy²
`√(9x^4 + 3x^3y - 5x^2y^2 + xy^3)`

2.) Divide using normal division rules, but it's super hard now 'cause there are letters involved. Basically, what can you multiply 3x³ by to get 9x⁴? 3x. So 3x is your first number. Then multiply everything else by 3x, and subtract

3x

3x³ + 2x²y - xy²
`√(9x^4 + 3x^3y - 5x^2y^2 + xy^3)`

-(9x⁴ + 6x³y - 3x²y²)

= 0 - 3x³y - 2x²y² - 5x²y + xy³

Now lets do that again, see what happens. 3x³ times -y should get -3x³y

3x - y

3x³ + 2x²y - xy²
`√(9x^4 + 3x^3y - 5x^2y^2 + xy^3)`

- (9x⁴ + 6x³y - 3x²y²)

= 0 - 3x³y - 2x²y² - 5x²y + xy³

- ( - 3x³y - 2x²y² + xy³)

= 0 + 0 - 5x²y + 0

So! From this information, we can know that the answer is 3x-y with a remainder of - 5x²y. How it's written is shown above, in "Answer"