3. If $$ t=-2 $$, then $$ t^{3}-2 t^{2}+5 t-3= $$ ?

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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**.
When $$ t = -2 $$, the expression $$ t^{3} - 2t^{2} + 5t - 3 $$ equals **-29**.

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