To find the zeros of the function [tex]\( f(x) = (2x + 6)(x - 4) \)[/tex], we need to determine the values of [tex]\( x \)[/tex] where [tex]\( f(x) = 0 \)[/tex].
The product of two factors is zero if and only if at least one of the factors is zero. Therefore, we set each factor in the equation to zero and solve for [tex]\( x \)[/tex] individually.
1. Set the first factor [tex]\( 2x + 6 = 0 \)[/tex]:
[tex]\[
2x + 6 = 0
\][/tex]
Subtract 6 from both sides:
[tex]\[
2x = -6
\][/tex]
Divide both sides by 2:
[tex]\[
x = -3
\][/tex]
2. Set the second factor [tex]\( x - 4 = 0 \)[/tex]:
[tex]\[
x - 4 = 0
\][/tex]
Add 4 to both sides:
[tex]\[
x = 4
\][/tex]
Hence, the zeros of the function [tex]\( f(x) = (2x + 6)(x - 4) \)[/tex] are [tex]\( x = -3 \)[/tex] and [tex]\( x = 4 \)[/tex].
Thus, the correct answer is:
C. [tex]\( x = -3 \)[/tex] and [tex]\( x = 4 \)[/tex].
