Answer :
To find the zeros of the polynomial function [tex]\( f(x) = -3x^5 - 2x^4 + 60x^3 + 40x^2 - 192x - 128 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
First, let's identify the zeros:
1. The polynomial can be factored or solved for zeros using specific techniques such as synthetic division, factoring, or numerical methods. Sometimes, when factoring is complex, numerical solutions like solving with software or graphing might provide quicker results.
2. Upon finding the zeros, we determine that the values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 0 \)[/tex] are:
- [tex]\( x = -4 \)[/tex]
- [tex]\( x = -2 \)[/tex]
- [tex]\( x = -\frac{2}{3} \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 4 \)[/tex]
So, the zeros of the function are [tex]\(-4, -2, -\frac{2}{3}, 2, 4\)[/tex]. These are the points where the graph of the polynomial will intersect the x-axis.
First, let's identify the zeros:
1. The polynomial can be factored or solved for zeros using specific techniques such as synthetic division, factoring, or numerical methods. Sometimes, when factoring is complex, numerical solutions like solving with software or graphing might provide quicker results.
2. Upon finding the zeros, we determine that the values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 0 \)[/tex] are:
- [tex]\( x = -4 \)[/tex]
- [tex]\( x = -2 \)[/tex]
- [tex]\( x = -\frac{2}{3} \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 4 \)[/tex]
So, the zeros of the function are [tex]\(-4, -2, -\frac{2}{3}, 2, 4\)[/tex]. These are the points where the graph of the polynomial will intersect the x-axis.
