Question

Divide f(x) by d(x), and write a summary statement in the form indicated.

Answer 1

Answer:

$x^{2} +5x-3$

Step-by-step explanation:

If we divide these two polynomials, we would have:

$\frac{x^{4}+5x^{3}-2x^{2}+5x-3}{x^{2}+1}=x^{2} +5x-3$

To do a long division form, we have to divide term by term, like its shown in the image.

Using the image is better that writing it down here, because this doesn't have a format to divide polynomials.

Therefore, the answer is:

$x^{2} +5x-3$

Answer 2

F ( x ) : d ( x ) =
( x^4 + 5 x³ - 2 x² + 5 x - 3 ) : ( x² + 1 ) = x² + 5 x - 3 
- x^4           - x²
-----------------------
           5 x³ - 3 x²
         - 5 x²          - 5 x
        ----------------------------
                  - 3 x²         - 3
                 + 3 x²         + 3
               ---------------------
                R ( x ) = 0
Answer: x² + 5 x - 3