(5x^3 - 2x^2 + 3) / (x^2 + 4)
x^2 + 4 doesn't factor.
Let's do synthestic division:
|
|
|
|
|
5x |
-2 |
x^2 |
+0x |
+4 |
5x^3 |
-2x^2 |
+0x |
+3 |
|
|
|
-(5x^3 |
+0x |
+20x) |
|
|
|
|
|
-2x^2 |
-20x |
+3 |
|
|
|
|
-(-2x^2 |
+0x |
-8) |
|
|
|
|
|
-20x |
-5 |
(5x^3 - 2x^2 + 3) / (x^2 + 4) = 5x - 2 - 5(4x+1)/(x^2+4)
(5x^3 - 2x^2 + 3) / (x^2 + 4) doesn't work out evenly.
x^2 + 4 is not a factor of 5x^3 - 2x^2 + 3
Answer: 5x - 2 - 5(4x+1)/(x^2+4)