Questions: If t=-3, then 3t^2+5t+6 equals (a) -36 (b) -6 (c) 6 (d) 18

Solution Steps

To solve the given expression \(3t^2 + 5t + 6\) for \(t = -3\), we need to substitute \(-3\) for \(t\) in the expression and then evaluate it.

We start with the expression \( 3t^2 + 5t + 6 \). To find its value when \( t = -3 \), we substitute \(-3\) for \( t \):

\[ 3(-3)^2 + 5(-3) + 6 \]

First, calculate \( (-3)^2 \):

\[ (-3)^2 = 9 \]

Next, multiply by 3:

\[ 3 \times 9 = 27 \]

Then, calculate \( 5(-3) \):

\[ 5 \times (-3) = -15 \]

Finally, add all the terms together:

\[ 27 + (-15) + 6 = 27 - 15 + 6 = 18 \]

Final Answer