To determine the zeros of function [tex]\( g \)[/tex] given its factors [tex]\((x-7)\)[/tex] and [tex]\((x+6)\)[/tex], we need to find the values of [tex]\( x \)[/tex] that make each factor equal to zero. This is because the zeros of a function are the values of [tex]\( x \)[/tex] for which the function equals zero.
1. Consider the factor [tex]\((x-7)\)[/tex]:
- Set [tex]\( x-7 = 0 \)[/tex],
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 7 \)[/tex].
2. Now consider the factor [tex]\((x+6)\)[/tex]:
- Set [tex]\( x+6 = 0 \)[/tex],
- Solve for [tex]\( x \)[/tex]: [tex]\( x = -6 \)[/tex].
The values of [tex]\( x \)[/tex] that make the function [tex]\( g \)[/tex] equal to zero are [tex]\( x = 7 \)[/tex] and [tex]\( x = -6 \)[/tex].
Thus, the zeros of the function [tex]\( g \)[/tex] are:
B. -6 and 7
