Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Find the error in the calculations below, if there is one:

Line (1): [tex]4x^3 + 2x^2 - 6x + 3[/tex]
Line (2): [tex]= 2x^2(2x + 1) - 3(2x + 1)[/tex]
Line (3): [tex]= 2x^2(2x + 1) + (-3)(2x + 1)[/tex]
Line (4): [tex]= (2x^2 - 3)(2x + 1)[/tex]

A. The error occurred from line (1) to line (2).
B. The error occurred from line (2) to line (3).
C. There are no errors.
D. The error occurred from line (3) to line (4).

Sagot :

GinnyAnswer
To determine if there is any error in the given steps, let's examine each transformation step-by-step:

### Line (1)
[tex]\[ 4x^3 + 2x^2 - 6x + 3 \][/tex]

### Line (2)
[tex]\[ = 2x^2(2x + 1) - 3(2x + 1) \][/tex]

To verify the correctness of the step from Line (1) to Line (2), we need to expand and simplify the expression in Line (2).

Expanding Line (2):
[tex]\[ 2x^2(2x + 1) - 3(2x + 1) \][/tex]

Distribute each term inside the parentheses:
[tex]\[ (2x^2 \cdot 2x) + (2x^2 \cdot 1) - (3 \cdot 2x) - (3 \cdot 1) \][/tex]
[tex]\[ = 4x^3 + 2x^2 - 6x - 3 \][/tex]

Now compare this with Line (1):
[tex]\[ 4x^3 + 2x^2 - 6x + 3 \][/tex]
[tex]\[ 4x^3 + 2x^2 - 6x - 3 \][/tex]

It is clear that there is a discrepancy. The constants in Line (1) and the expanded Line (2) differ by a sign.
- Line (1) has \(+ 3\).
- Expanded Line (2) has \(- 3\).

Thus, there is an error in the step from Line (1) to Line (2).

### Summary
Given our detailed check, we see that an error occurred from Line (1) to Line (2). Therefore, the correct statement is:
- The error occurred from line (1) to line (2).

There are no needs to verify subsequent lines as the error has already been identified in the initial transformation from Line (1) to Line (2).
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.