To solve the expression [tex]\( z^2 - 2z + 15 \)[/tex] given [tex]\( z = 15 \)[/tex], let's substitute [tex]\( z \)[/tex] with 15 and work through the calculation step-by-step.
1. Substitute [tex]\( z \)[/tex] with 15 in the expression:
[tex]\[
15^2 - 2 \cdot 15 + 15
\][/tex]
2. Calculate [tex]\( 15^2 \)[/tex]:
[tex]\[
15^2 = 225
\][/tex]
3. Calculate [tex]\( -2 \cdot 15 \)[/tex]:
[tex]\[
-2 \cdot 15 = -30
\][/tex]
4. Combine the results:
[tex]\[
225 - 30 + 15
\][/tex]
5. Calculate [tex]\( 225 - 30 \)[/tex]:
[tex]\[
225 - 30 = 195
\][/tex]
6. Finally, add 15 to the result:
[tex]\[
195 + 15 = 210
\][/tex]
Thus, the value of the expression [tex]\( z^2 - 2z + 15 \)[/tex] when [tex]\( z = 15 \)[/tex] is [tex]\( 210 \)[/tex].
The correct answer is B) 210.
