Questions: d^3+3 d^2+15 d+21

Transcript text: $d^{3}+3 d^{2}+15 d+21$

Solution

Step 1: Evaluate the Polynomial

We need to evaluate the polynomial $d^3 + 3d^2 + 15d + 21$ for $d = 2$. Substituting $d$ into the polynomial gives us:

\[ 2^3 + 3(2^2) + 15(2) + 21 \]

Step 2: Calculate Each Term

Calculating each term separately:

Step 3: Sum the Results

Now, we sum all the calculated terms:

\[ 8 + 12 + 30 + 21 = 71 \]

The value of the polynomial $d^3 + 3d^2 + 15d + 21$ when $d = 2$ is

\[ \boxed{71} \]

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