Answer :
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].
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].
