Question

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

f(x) = x4 + 5x3 - 2x2 + 5x - 3; d(x) = x2 + 1

Answer 1

`x^(2) +5x-3`

Explanation:

If we divide these two polynomials, we would have:

`(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