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Jane evaluates [tex]$x^2 - 3x + 5[tex]$[/tex] for [tex]$[/tex]x = -2$[/tex] below.

Step 1: [tex]$(-2)^2 - 3(-2) + 5$[/tex]

Step 2: [tex]= 4 + 6 + 5[/tex]

Step 3: [tex]= 15[/tex]

What, if any, was Jane's mistake?

A. Jane made no mistakes.
B. Jane incorrectly evaluated [tex]$(-2)^2$[/tex] in step 2.
C. Jane incorrectly added the terms in step 3.
D. Jane incorrectly substituted in [tex]$x = -2$[/tex] in step 1.

Sagot :

GinnyAnswer
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.
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