Sure, let's evaluate the expression \( 2x^3 - 3x^2 + 4 \) for \( x = -2 \).
1. First, substitute \( x = -2 \) into the expression:
[tex]\[
2(-2)^3 - 3(-2)^2 + 4
\][/tex]
2. Next, calculate the cube of \(-2\):
[tex]\[
(-2)^3 = -8
\][/tex]
3. Now, multiply this result by 2:
[tex]\[
2 \cdot (-8) = -16
\][/tex]
4. Then, calculate the square of \(-2\):
[tex]\[
(-2)^2 = 4
\][/tex]
5. Next, multiply this result by 3:
[tex]\[
3 \cdot 4 = 12
\][/tex]
6. Combine all parts of the expression:
[tex]\[
-16 - 12 + 4
\][/tex]
7. Perform the addition and subtraction step by step:
[tex]\[
-16 - 12 = -28
\][/tex]
[tex]\[
-28 + 4 = -24
\][/tex]
Thus, the value of the expression [tex]\( 2x^3 - 3x^2 + 4 \)[/tex] when [tex]\( x = -2 \)[/tex] is [tex]\( -24 \)[/tex].
