Let's carefully go through Jane's steps to evaluate the expression \( x^2 - 3x + 5 \) for \( x = -2 \).
Step 1: Substitute \( x = -2 \) into the equation.
[tex]\[ (-2)^2 - 3(-2) + 5 \][/tex]
At this point, Jane correctly substituted \(-2\) for \(x\).
Step 2: Compute each term in the expression.
[tex]\[ (-2)^2 \][/tex]
[tex]\[ -3(-2) \][/tex]
[tex]\[ + 5 \][/tex]
Calculate each term individually:
1. \( (-2)^2 = 4 \)
2. \( -3(-2) = 6 \)
3. \( + 5 \)
So the expression becomes:
[tex]\[ 4 + 6 + 5 \][/tex]
However, Jane evaluated the terms as:
[tex]\[ (-2)^2 - 3(-2) + 5 = -4 + 6 + 5 \][/tex]
This is incorrect because Jane evaluated \( (-2)^2 \) as \(-4\), which is wrong. The correct evaluation is \(4\).
Step 3: Add the terms together.
The correct addition of the terms:
[tex]\[ 4 + 6 + 5 = 15 \][/tex]
Therefore, Jane's mistake was in Step 2, where she incorrectly evaluated \( (-2)^2 \). Hence, the correct statement is:
Jane incorrectly evaluated [tex]\((-2)^2\)[/tex] in step 2.
