The solution to the polynomial division is:
y = (x + 8) + (26/(x - 3))
The end behavior of the polynomial is:
As x → +∞, y → +∞
As x → -∞, y → -∞
What is the end behavior of the Polynomial?
1) The polynomial expression is given as:
c(x) = (x² + 5x + 2)/(x - 3)
Using polynomial long division gives us:
x + 8
(x - 3) | x² + 5x + 2
- x² - 3x
8x + 2
- 8x - 24
26
Thus, the solution is:
y = (x + 8) + (26/(x - 3))
2) The end behavior refers to the behavior of the graph of a function at the "ends" of the x-axis, or as x approaches positive or negative infinity.
In this case:
As x → +∞, y → +∞
As x → -∞, y → -∞