One zero of f(x)=2x3−x2−2x+1 is -1. What are the other zeros of the function? (1 point) Responses 1 and 12 1 and 1 half 1 and 2 1 and 2 2 and 12 2 and 1 half 1 and 3
If one zero of the function f(x) = 2x^3 - x^2 - 2x + 1 is -1, we can use synthetic division or polynomial division to determine the other zeros.
Let's use synthetic division:
-1 | 2 -1 -2 1
| -2 3 -1
-----------------
2 -3 1 0
The resulting quotient polynomial is 2x^2 - 3x + 1. We can now find the zeros of this polynomial by factoring or by using the quadratic formula.
Let's try to factor:
2x^2 - 3x + 1 = (2x - 1)(x - 1)
Setting each factor equal to zero gives us the other zeros:
2x - 1 = 0 => x = 1/2
x - 1 = 0 => x = 1
So, the other zeros of the function f(x) = 2x^3 - x^2 - 2x + 1 are 1/2 and 1. The correct answer is "1 and 1/2".