Answer:
- x+2 is a factor
- y = (x +4)(x +2)(x -2)
Step-by-step explanation:
You want the complete factorization of x³ +4x² -4x -16.
Factor by pairs
Pairing terms of the given polynomial, we have ...
(x³ +4x²) -(4x +16)
Factoring each pair gives ...
x²(x +4) -4(x +4)
= (x² -4)(x +4)
Difference of squares
The factorization of x² -4 is found using the form for factoring the difference of squares:
a² -b² = (a +b)(a -b)
x² -4 = (x +2)(x -2)
Note that x+2 is a factor here.
Complete factorization
The complete factorization of the given polynomial is ...
x³ +4x² -4x -16 = (x +4)(x +2)(x -2)
This is confirmed by the graph, which shows zeros at x = -4, -2, 2.
