Evaluate the expression for each value of \( x \). \[ x^{3}-4 x^{2}-x+8 \] (a) \( x=4 \) \( \square \) \[ 60 \] (b) \( x=-4 \) \( \square \) \[ 52 \] SUBMIT ANSWER

It appears there may be some errors in your evaluations of the expression \( x^{3} - 4x^{2} - x + 8 \). Let's re-evaluate the expression for each given value of \( x \). --- ### (a) \( x = 4 \) **Calculation:** \[ \begin{align*} x^{3} - 4x^{2} - x + 8 &= 4^{3} - 4(4)^{2} - 4 + 8 \\ &= 64 - 4(16) - 4 + 8 \\ &= 64 - 64 - 4 + 8 \\ &= (64 - 64) + (-4 + 8) \\ &= 0 + 4 \\ &= 4 \end{align*} \] **Result:** \( 4 \) **Your Answer:** \( 60 \) **Correction:** The correct value is **4**, not **60**. --- ### (b) \( x = -4 \) **Calculation:** \[ \begin{align*} x^{3} - 4x^{2} - x + 8 &= (-4)^{3} - 4(-4)^{2} - (-4) + 8 \\ &= -64 - 4(16) + 4 + 8 \\ &= -64 - 64 + 4 + 8 \\ &= (-64 - 64) + (4 + 8) \\ &= -128 + 12 \\ &= -116 \end{align*} \] **Result:** \( -116 \) **Your Answer:** \( 52 \) **Correction:** The correct value is **-116**, not **52**. --- ### Summary - **For \( x = 4 \):** The expression evaluates to **4**. - **For \( x = -4 \):** The expression evaluates to **-116**. If you have any further questions or need additional assistance with these calculations, feel free to ask!