Question
3. If \( t=-2 \), then \( t^{3}-2 t^{2}+5 t-3= \) ?
Ask by Tran Moreno. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
When \( t = -2 \), the expression \( t^{3} - 2t^{2} + 5t - 3 \) equals **-29**.
Solution
To evaluate the polynomial \( t^{3} - 2t^{2} + 5t - 3 \) at \( t = -2 \), follow these steps:
1. **Substitute \( t = -2 \) into the polynomial:**
\[
(-2)^{3} - 2(-2)^{2} + 5(-2) - 3
\]
2. **Calculate each term individually:**
- \( (-2)^{3} = -8 \)
- \( -2(-2)^{2} = -2(4) = -8 \) (since \( (-2)^2 = 4 \))
- \( 5(-2) = -10 \)
- \( -3 \) remains as is.
3. **Combine all the calculated terms:**
\[
-8 - 8 - 10 - 3
\]
4. **Add them together:**
\[
-8 - 8 = -16 \\
-16 - 10 = -26 \\
-26 - 3 = -29
\]
**Final Answer:** \( t^{3} - 2t^{2} + 5t - 3 \) evaluated at \( t = -2 \) is **-29**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the value of the expression \( t^{3}-2 t^{2}+5 t-3 \) when \( t = -2 \), we will substitute \(-2\) into the expression: \[ t^{3} = (-2)^{3} = -8, \] \[ -2 t^{2} = -2 \cdot (-2)^{2} = -2 \cdot 4 = -8, \] \[ 5 t = 5 \cdot (-2) = -10, \] Now, combining all the parts: \[ -8 - 8 - 10 - 3 = -29. \] Thus, the value of the expression is \(-29\).
