Answer
Thr factors include
(x + 5)
(x + 3)
(x + 1)
The zeros include
x = -5
x = -3
x = -1
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!!!
