To determine the zero of the polynomial [tex]\( f(x) = 3x + 7 \)[/tex], we need to find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex]. Here are the steps to solve this problem:
1. Set the polynomial equal to zero:
We start with the equation:
[tex]\[
3x + 7 = 0
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we first need to move the constant term to the other side of the equation. Subtract 7 from both sides:
[tex]\[
3x + 7 - 7 = 0 - 7
\][/tex]
Simplifying this, we get:
[tex]\[
3x = -7
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Now, divide both sides of the equation by 3 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-7}{3}
\][/tex]
Thus, the zero of the polynomial [tex]\( f(x) = 3x + 7 \)[/tex] is:
[tex]\[
x = -\frac{7}{3}
\][/tex]
