Discover the best answers to your questions with the help of IDNLearn.com. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.
Sagot :
Let's analyze Julian's work step by step to identify where the first mistake occurs.
1. Given Expression:
[tex]\[ 2 x^4 + 2 x^3 - x^2 - x \][/tex]
2. Step 1:
[tex]\[ = x\left(2 x^3 + 2 x^2 - x - 1\right) \][/tex]
3. Step 2:
[tex]\[ = x\left[2 x^2(x + 1) - 1(x - 1)\right] \][/tex]
Here, Julian attempts to factor by grouping. He separates the terms into two groups:
[tex]\[ 2 x^3 + 2 x^2 \quad \text{and} \quad - x - 1 \][/tex]
He then factors [tex]\(2 x^2\)[/tex] from the first group and [tex]\(-1\)[/tex] from the second group:
[tex]\[ = x \left[2 x^2(x + 1) - 1(x - 1)\right] \][/tex]
Upon examining this step, we can see that the factoring is done incorrectly.
- For the first part of the expression, Julian correctly factors [tex]\(2 x^2\)[/tex] out of [tex]\(2 x^3 + 2 x^2\)[/tex], resulting in [tex]\(2 x^2 (x + 1)\)[/tex].
- For the second part, when factoring out [tex]\(-1\)[/tex] from [tex]\(- x - 1\)[/tex], it should have been [tex]\(-1 (x + 1)\)[/tex] (factoring [tex]\(-1\)[/tex] correctly here).
Therefore, Julian's factoring of the second term [tex]\(-x - 1\)[/tex] to [tex]\(-1 (x - 1)\)[/tex] was incorrect. It should have been:
[tex]\[ -1 (x + 1) \][/tex]
4. Step 3 (Julian's Incorrect Work):
[tex]\[ = x\left(2 x^2 - 1\right)(x + 1)(x - 1) \][/tex]
Since the step that includes the error is Step 2, the correct statement that describes Julian’s mistake is:
Statement 4: Julian incorrectly factored [tex]\(2 x^2\)[/tex] from the first group of terms.
Thus, Julian made the first mistake at Step 2.
1. Given Expression:
[tex]\[ 2 x^4 + 2 x^3 - x^2 - x \][/tex]
2. Step 1:
[tex]\[ = x\left(2 x^3 + 2 x^2 - x - 1\right) \][/tex]
3. Step 2:
[tex]\[ = x\left[2 x^2(x + 1) - 1(x - 1)\right] \][/tex]
Here, Julian attempts to factor by grouping. He separates the terms into two groups:
[tex]\[ 2 x^3 + 2 x^2 \quad \text{and} \quad - x - 1 \][/tex]
He then factors [tex]\(2 x^2\)[/tex] from the first group and [tex]\(-1\)[/tex] from the second group:
[tex]\[ = x \left[2 x^2(x + 1) - 1(x - 1)\right] \][/tex]
Upon examining this step, we can see that the factoring is done incorrectly.
- For the first part of the expression, Julian correctly factors [tex]\(2 x^2\)[/tex] out of [tex]\(2 x^3 + 2 x^2\)[/tex], resulting in [tex]\(2 x^2 (x + 1)\)[/tex].
- For the second part, when factoring out [tex]\(-1\)[/tex] from [tex]\(- x - 1\)[/tex], it should have been [tex]\(-1 (x + 1)\)[/tex] (factoring [tex]\(-1\)[/tex] correctly here).
Therefore, Julian's factoring of the second term [tex]\(-x - 1\)[/tex] to [tex]\(-1 (x - 1)\)[/tex] was incorrect. It should have been:
[tex]\[ -1 (x + 1) \][/tex]
4. Step 3 (Julian's Incorrect Work):
[tex]\[ = x\left(2 x^2 - 1\right)(x + 1)(x - 1) \][/tex]
Since the step that includes the error is Step 2, the correct statement that describes Julian’s mistake is:
Statement 4: Julian incorrectly factored [tex]\(2 x^2\)[/tex] from the first group of terms.
Thus, Julian made the first mistake at Step 2.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.