SOLUTION: Is it possible to subtract two polynomials, each of degree 3, and have the difference be a polynomial of degree 2? If yes, give an example. Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Is it possible to subtract two polynomials, each of degree 3, and have the difference be a polynomial of degree 2? If yes, give an example. Thanks      Log On


   



Question 1076262: Is it possible to subtract two polynomials, each of degree 3, and have the difference be a polynomial of degree 2? If yes, give an example. Thanks
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Yes.  Just make them so that when you subtract them,
their x3 terms will cancel and leave terms
in x2.

Example"

P%28x%29=x%5E3%2B2x%5E2%2B3x%2B2 and Q%28x%29=x%5E3%2Bx%5E2%2B2x%2B1

Then

P%28x%29-Q%28x%29=%28x%5E3%2B2x%5E2%2B3x%2B2%29-%28x%5E3%2Bx%5E2%2B2x%2B1%29

P%28x%29-Q%28x%29=x%5E3%2B2x%5E2%2B3x%2B2-x%5E3-x%5E2-2x-1%29

P%28x%29-Q%28x%29=x%5E2%2Bx%2B1%29

Edwin