To find the zeros of the function [tex]\( f(x) = (x-1)(x+6) \)[/tex], we need to determine the values of [tex]\( x \)[/tex] that make [tex]\( f(x) \)[/tex] equal to zero. A zero of the function is a value of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
Given the function:
[tex]\[ f(x) = (x-1)(x+6) \][/tex]
To find the zeros:
1. Set [tex]\( f(x) \)[/tex] equal to zero:
[tex]\[ (x-1)(x+6) = 0 \][/tex]
2. The product of two factors is zero if and only if at least one of the factors is zero. Thus, we solve the equation by setting each factor equal to zero:
- First factor:
[tex]\[ x-1 = 0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = 1 \][/tex]
- Second factor:
[tex]\[ x+6 = 0 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = -6 \][/tex]
Therefore, the zeros of the function [tex]\( f(x) = (x-1)(x+6) \)[/tex] are [tex]\( x = 1 \)[/tex] and [tex]\( x = -6 \)[/tex].
So, among the given options, the correct answers are:
C. [tex]\( x = 1 \)[/tex]
D. [tex]\( x = -6 \)[/tex]
