Find the quotient using long division

Question

x^4+6x^2+2/x^2+1

Answer 1

When dividing, you want to make sure you have all the term in descending order.  If you do not see a term with a variable, then the coefficient is zero.

 

 

                        x² + 0x  + 5

             ______________________

(x² + 1) | x⁴ + 0x³ + 6x² + 0x + 2

               x⁴          +  x²

              ________________

                      0x³ + 5x²

                                 0

                      _________________

                               5x²          + 2

                               5x²          + 5

                               _____________

                                                -3

 

Quotient = x² + 5

Remainder = -3

 

Now we check.

 

(x² + 5)(x² + 1) - 3 =

 

x⁴ + 6x² + 5 - 3 =

 

x⁴ + 6x² + 2

 

 

This checks out!!

Answer 2

I advise you to examine examples of polynomial Long Division; these may be found in any good Algebra book or in online resources.

 

Be sure to make room for missing terms (of degree 3 and 1) in the dividend.