Answer
Thr factors include
(x + 5)
(x + 3)
(x + 1)
The zeros include
x = -5
x = -3
x = -1
Step-by-step explanation
The zeros of the polynomial are obtainable from the factors of the polynomial.
So, to solve this and obtain the remaining factors, we will use the given factor, (x + 5), to divide the polynomial, x³ + 9x² + 23x + 15
So,
x³ + 9x² + 23x + 15 = (x + 5) (x² + 4x + 3)
We can then reduce the other part further
x² + 4x + 3
= x² + x + 3x + 3
= x (x + 1) + 3 (x + 1)
= (x + 3) (x + 1)
So, the poilynomial broken in to its factors is
x³ + 9x² + 23x + 15 = (x + 5) (x + 3) (x + 1)
So, we can find the zeros now
x + 5 = 0
x = -5
x + 3 = 0
x = -3
x + 1 = 0
x = -1
Hope this Helps!!!