Step-by-step explanation:
what the other answer tries to say is that it proves that x = -5 is a 0 point of the function P(x).
and that means that (x + 5) is a factor.
because the factors of such a polynomial are the terms of x that would bring the whole expression to 0.
so, but now to the actual division :
x³ + 2x² - 13x + 10 ÷ x + 5 = x² - 3x + 2
- x³ + 5x²
-----------------
0 - 3x² - 13x
- - 3x² - 15x
------------------------
0 2x + 10
- 2x + 10
------------------------------
0 0
as the remainder is 0, this shows that (x + 5) is a factor.
