Evaluating the Expression

We are given an algebraic expression and a specific value for the variable \(x\). Our task is to substitute this value into the expression and calculate the result.

The given expression is:

\(x^2 + 2x + 5\)

The given value for \(x\) is:

\(x = 3\)

Steps to Evaluate the Expression

To find the value of the expression when \(x = 3\), we substitute 3 for every instance of \(x\) in the expression.

1. Substitute \(x=3\) into the expression \(x^2 + 2x + 5\).
2. Calculate each term separately.
3. Add the results together.

Let's substitute \(x = 3\) into the expression:

\((3)^2 + 2(3) + 5\)

Now, we calculate each part:

• First term: \(x^2\) becomes \((3)^2\). The square of 3 is \(3 \times 3\).
• \((3)^2 = 9\)
• Second term: \(2x\) becomes \(2(3)\). Multiply 2 by 3.
• \(2(3) = 6\)
• Third term: The constant term is 5.

Now, we add the values of the terms together:

\(9 + 6 + 5\)

Performing the addition:

\(9 + 6 = 15\)

\(15 + 5 = 20\)

So, the value of the expression \(x^2 + 2x + 5\) when \(x = 3\) is 20.

Checking the Options

Let's compare our result with the given options:

Our calculated value, 20, matches Option 2.