Lilygrimm06idn
Answered

Get the information you need from a community of experts on IDNLearn.com. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

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

Step 1: [tex]$(-2)^2-3(-2)+5$[/tex]
Step 2: [tex][tex]$=4+6+5$[/tex][/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][tex]$x=-2$[/tex][/tex] in step 1.

Sagot :

GinnyAnsweridn
To evaluate the expression [tex]\(x^2 - 3x + 5\)[/tex] for [tex]\(x = -2\)[/tex], let's follow the steps:

1. Substitute [tex]\(x = -2\)[/tex] into the expression:
[tex]\[ (-2)^2 - 3(-2) + 5 \][/tex]

2. Evaluate each part of the expression:

- [tex]\((-2)^2\)[/tex]:
[tex]\[ (-2)^2 = (-2) \times (-2) = 4 \][/tex]

- [tex]\(-3(-2)\)[/tex]:
[tex]\[ -3 \times (-2) = 6 \][/tex]

- The constant term remains:
[tex]\[ 5 \][/tex]

So, the expression now is:
[tex]\[ 4 + 6 + 5 \][/tex]

3. Add the terms together:
[tex]\[ 4 + 6 = 10 \][/tex]
[tex]\[ 10 + 5 = 15 \][/tex]

Thus, the correct evaluation of [tex]\(x^2 - 3x + 5\)[/tex] for [tex]\(x = -2\)[/tex] is 15.

Jane made a mistake in Step 2. Instead of evaluating [tex]\((-2)^2\)[/tex] correctly as 4, Jane incorrectly evaluated it as -4. Therefore, the correct answer is:

Jane incorrectly evaluated [tex]\((-2)^2\)[/tex] in Step 2.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.