Math / Algebra

QuestionThe movement of the progress bar moy be uneven because questions Find the error in the calculations below, if there is one: $\begin{array}{l} \text { Line }(1): 4 x^{3}+2 x^{2}-6 x+3 \\ \begin{array}{l} \text { Line }(2):=2 x^{2}(2 x+1)-3(2 x+1) \\ \text { Line (3): }=2 x^{2}(2 x+1)+(-3)(2 x+1) \\ \text { Line }(4):=\left(2 x^{2}-3\right)(2 x+1) \end{array} \end{array}$ There are no errors. The error occurred from line (2) to line (3). The error occurred from line (3) to line (4). The enror occurred from line (1) to line (2).

Studdy Solution

STEP 1

What is this asking? We need to find the mistake in factoring $4x^3 + 2x^2 - 6x + 3$ , if there is one! Watch out! Factoring can be tricky, so let's be super careful with the signs and make sure we're factoring correctly!

STEP 2

1. Analyze the first factoring attempt
2. Check the second factoring attempt
3. Verify the final factoring

STEP 3

Alright, so we're given $4x^3 + 2x^2 - 6x + 3$ .
In Line (1) to Line (2), they tried to factor by grouping.
They pulled out a $2x^2$ from the first two terms, which gives us $2x^2(2x + 1)$ .
That looks good so far.

STEP 4

Then, they tried to pull out a $-3$ from the last two terms.
If we do that correctly, we should get $-3(2x - 1)$ .
Uh oh, this is where the problem is!
They wrote $-3(2x + 1)$ instead, which is incorrect.
This changes the sign and messes up the whole factoring process.

STEP 5

Because of the mistake in the previous step, the rest of the factoring is incorrect.
Line (3) just rewrites Line (2) with an extra plus sign and parentheses around the $-3$ , which doesn't change anything.

STEP 6

Line (4) then factors out the common factor of $(2x + 1)$ , which would be correct if Line (2) and (3) were correct, but they aren't.
So, the final factored form $(2x^2 - 3)(2x + 1)$ is wrong.

STEP 7

Let's double-check by expanding the final factored form: $(2x^2 - 3)(2x + 1) = 2x^2(2x) + 2x^2(1) - 3(2x) - 3(1) = 4x^3 + 2x^2 - 6x - 3$ .

STEP 8

This result is almost the same as the original expression, but notice the last term is $-3$ instead of $3$ .
This confirms that the factoring was indeed incorrect.

STEP 9

The error occurred from Line (1) to Line (2) because they incorrectly factored out a $-3$ from $-6x + 3$ .
It should have been $-3(2x - 1)$ instead of $-3(2x + 1)$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the mistake in factoring $4x^3 + 2x^2 - 6x + 3$ , if there is one! Watch out! Factoring can be tricky, so let's be super careful with the signs and make sure we're factoring correctly!

STEP 2

1. Analyze the first factoring attempt
2. Check the second factoring attempt
3. Verify the final factoring

STEP 3

Alright, so we're given $4x^3 + 2x^2 - 6x + 3$ .
In Line (1) to Line (2), they tried to factor by grouping.
They pulled out a $2x^2$ from the first two terms, which gives us $2x^2(2x + 1)$ .
That looks good so far.

STEP 4

Then, they tried to pull out a $-3$ from the last two terms.
If we do that correctly, we should get $-3(2x - 1)$ .
Uh oh, this is where the problem is!
They wrote $-3(2x + 1)$ instead, which is incorrect.
This changes the sign and messes up the whole factoring process.

STEP 5

Because of the mistake in the previous step, the rest of the factoring is incorrect.
Line (3) just rewrites Line (2) with an extra plus sign and parentheses around the $-3$ , which doesn't change anything.

STEP 6

Line (4) then factors out the common factor of $(2x + 1)$ , which would be correct if Line (2) and (3) were correct, but they aren't.
So, the final factored form $(2x^2 - 3)(2x + 1)$ is wrong.

STEP 7

Let's double-check by expanding the final factored form: $(2x^2 - 3)(2x + 1) = 2x^2(2x) + 2x^2(1) - 3(2x) - 3(1) = 4x^3 + 2x^2 - 6x - 3$ .

STEP 8

This result is almost the same as the original expression, but notice the last term is $-3$ instead of $3$ .
This confirms that the factoring was indeed incorrect.

STEP 9

The error occurred from Line (1) to Line (2) because they incorrectly factored out a $-3$ from $-6x + 3$ .
It should have been $-3(2x - 1)$ instead of $-3(2x + 1)$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the mistake in factoring 4x3+2x2−6x+34x^3 + 2x^2 - 6x + 34x3+2x2−6x+3, if there is one! Watch out! Factoring can be tricky, so let's be super careful with the signs and make sure we're factoring correctly!

STEP 2

1. Analyze the first factoring attempt2. Check the second factoring attempt3. Verify the final factoring

STEP 3

Alright, so we're given 4x3+2x2−6x+34x^3 + 2x^2 - 6x + 34x3+2x2−6x+3.In Line (1) to Line (2), they tried to factor by grouping.They pulled out a 2x22x^22x2 from the first two terms, which gives us 2x2(2x+1)2x^2(2x + 1)2x2(2x+1).That looks good so far.

STEP 4

STEP 5

Because of the mistake in the previous step, the rest of the factoring is incorrect.Line (3) just rewrites Line (2) with an extra plus sign and parentheses around the −3-3−3, which doesn't change anything.

STEP 6

Line (4) then factors out the common factor of (2x+1)(2x + 1)(2x+1), which would be correct if Line (2) and (3) were correct, but they aren't.So, the final factored form (2x2−3)(2x+1)(2x^2 - 3)(2x + 1)(2x2−3)(2x+1) is wrong.

STEP 7

Let's double-check by expanding the final factored form: (2x2−3)(2x+1)=2x2(2x)+2x2(1)−3(2x)−3(1)=4x3+2x2−6x−3(2x^2 - 3)(2x + 1) = 2x^2(2x) + 2x^2(1) - 3(2x) - 3(1) = 4x^3 + 2x^2 - 6x - 3(2x2−3)(2x+1)=2x2(2x)+2x2(1)−3(2x)−3(1)=4x3+2x2−6x−3.

STEP 8

This result is almost the same as the original expression, but notice the last term is −3-3−3 instead of 333.This confirms that the factoring was indeed incorrect.

STEP 9

The error occurred from Line (1) to Line (2) because they incorrectly factored out a −3-3−3 from −6x+3-6x + 3−6x+3.It should have been −3(2x−1)-3(2x - 1)−3(2x−1) instead of −3(2x+1)-3(2x + 1)−3(2x+1).

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the mistake in factoring $4x^3 + 2x^2 - 6x + 3$ , if there is one! Watch out! Factoring can be tricky, so let's be super careful with the signs and make sure we're factoring correctly!

1. Analyze the first factoring attempt
2. Check the second factoring attempt
3. Verify the final factoring

Alright, so we're given $4x^3 + 2x^2 - 6x + 3$ .
In Line (1) to Line (2), they tried to factor by grouping.
They pulled out a $2x^2$ from the first two terms, which gives us $2x^2(2x + 1)$ .
That looks good so far.

Because of the mistake in the previous step, the rest of the factoring is incorrect.
Line (3) just rewrites Line (2) with an extra plus sign and parentheses around the $-3$ , which doesn't change anything.

Line (4) then factors out the common factor of $(2x + 1)$ , which would be correct if Line (2) and (3) were correct, but they aren't.
So, the final factored form $(2x^2 - 3)(2x + 1)$ is wrong.

Let's double-check by expanding the final factored form: $(2x^2 - 3)(2x + 1) = 2x^2(2x) + 2x^2(1) - 3(2x) - 3(1) = 4x^3 + 2x^2 - 6x - 3$ .

This result is almost the same as the original expression, but notice the last term is $-3$ instead of $3$ .
This confirms that the factoring was indeed incorrect.

The error occurred from Line (1) to Line (2) because they incorrectly factored out a $-3$ from $-6x + 3$ .
It should have been $-3(2x - 1)$ instead of $-3(2x + 1)$ .