Answer:
3x - y + [tex]\frac{- 5x^2y}{3x^3 + 2x^2y - xy^2}[/tex]
Step-by-step explanation:
Hooboy okay here we go.
1.) Rewrite the equation in the classic division method
3x³ + 2x²y - xy² [tex]\sqrt{9x^4 + 3x^3y - 5x^2y^2 + xy^3}[/tex]
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 [tex]\sqrt{9x^4 + 3x^3y - 5x^2y^2 + xy^3}[/tex]
-(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 [tex]\sqrt{9x^4 + 3x^3y - 5x^2y^2 + xy^3}[/tex]
- (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"
