9x^2+5x+2/4x+1

Question

so i need help answering this q i would be extremely grateful if you showed me step by step on this problem. i would prefer if you used long divsion

Answer 1

It took me awhile to understand the question. The polynomial 

9x^2+5x+2

is being divided by 4x+1

 

4x+1| 9x^2+5x+2

 

If you multiply the 4x polynomial by 9x/4 the product will yield the term 9x^2 The first term of the second order polynomial so let's try that

 

          9x/4

4x+1| 9x^2+5x+2

          9x^2+9x/4

 

The bottom line is the product of (4x+1) and 9x/4

 

as in long division subtract

 

          9x/4
4x+1| 9x^2+5x.    +2
          9x^2+9x/4

                    11x/4   +2

this last line is the difference of the second order polynomial and the polynomial resulting from the product of 9x/2 and 4x+1

 

now if we multiply by 11/16 we will get the 11x/4 term

 

 

 

          9x/4+11/16
4x+1| 9x^2+5x. +2
          9x^2+9x/4
                  11x/4. +2

                  11x/4+11/16

                             21/16

 

 

21/16 is the remainder after the long division. 

 

9x^2+5x+2

=(9x/4+11/16)(4x+1)+21/16

 

to check multiply out the right hand side 

 

=9x^2

      +9x/4+11x/4

      +11/16+21/16

 

yep checks out!

 

or rewriting by dividing by (4x+1)

 

(9x^2+5x+2)/(4x+1)
=(9x/4+11/16)

              +21/[16(4x+1)]