x^3 - 2*x^2 + 2*x - 4 / x^2 + 2

Question

Long Division of Algebraic Polynomials

Answer 1

What is the question asking exactly? Are you trying to solve the equation or you trying to break up this polynomial into smaller equations? Oh, I see what you are doing.

 

So, first, here is my advice: use parentheses. 

 

The equation should be written as: (x^3 - 2*x^2 + 2*x - 4)/(x^2 + 0*x + 2)

1. We are given a 3 exponent polynomial over a 2 exponent polynomial, which means the the quotient is a 1 exponent polynomial.
2. First we divide the denominator into the numerator as such: since the denominator has 3 variables, we will compute it as normal long division.

• x^2 + 0*x + 2 into x^3 - 2*x^2 + 2*x gives us x with a remainder of -2*x^2 - 0*x - 4
• x^2 + 0*x + 2 into the remainder, -2*x^2 - 0*x - 4, gives us -2 with no remainder

 

This leaves us with the quotient of x - 2. This works with our expectation that the quotient should be a 1 exponent polynomial. 

Answer 2

Using long division it gives

 

(x-2)