a. Watch this video of Mrs. Hool completing a similar problem
b. Reattempt the question from your test:
i. Elijah is solving the quadratic equation by factoring.
His work is shown below. In which step did Elijah make his first error? What
is it?

Step 1:3x
Step 2:
Step 3:
Step
Step or
or

Ask by Robbins Reed. in the United States

Jan 24,2025

Question

a. Watch this video of Mrs. Hool completing a similar problem
b. Reattempt the question from your test:
i. Elijah is solving the quadratic equation by factoring.
His work is shown below. In which step did Elijah make his first error? What
is it?

Step 1:3x
Step 2:
Step 3:
Step
Step or
or

Ask by Robbins Reed. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To determine where Elijah made his first error in solving the quadratic equation $$ 3 x^{2}-14 x-24=0 $$ by factoring, let's analyze each step of his work.

1. **Original Equation**: 
   $$
   3 x^{2}-14 x-24=0
   $$

2. **Step 1**: Elijah writes $$ 3x $$. This step is unclear and does not provide any useful information.

3. **Step 2**: 
   $$
   (3 x^{2}-4 x)+(18 x-24)=0
   $$
   Here, Elijah attempts to group the terms. However, the grouping is incorrect. The correct grouping should maintain the original equation's structure. The term $$ -14x $$ should be split into two terms that add up to $$ -14x $$ while also considering the product of the leading coefficient and the constant term.

4. **Step 3**: 
   $$
   x(3 x-4)+6(3 x-4)=0
   $$
   This step is based on the incorrect grouping from Step 2. Therefore, it is also incorrect.

5. **Step 4**: 
   $$
   (3 x-4)(x+6)=0
   $$
   This step is derived from the previous incorrect step.

6. **Step 5**: 
   $$
   3 x-4=0 \quad \text{or} \quad x+6=0
   $$
   This leads to the solutions $$ x=\frac{4}{3} $$ or $$ x=6 $$.

### Conclusion:
Elijah's first error occurred in **Step 2**, where he incorrectly grouped the terms. The correct approach would involve factoring the quadratic expression directly or using the quadratic formula.

To find the correct factors, we can use the method of factoring directly from the original equation:

1. The product of $$ a $$ (3) and $$ c $$ (-24) is $$ -72 $$.
2. We need two numbers that multiply to $$ -72 $$ and add to $$ -14 $$. The correct pair is $$ -18 $$ and $$ 4 $$.
3. Thus, we can rewrite the equation as:
   $$
   3x^2 - 18x + 4x - 24 = 0
   $$
4. Factoring gives:
   $$
   3x(x - 6) + 4(x - 6) = 0
   $$
5. This leads to:
   $$
   (3x + 4)(x - 6) = 0
   $$

The correct solutions would then be:
$$
3x + 4 = 0 \quad \Rightarrow \quad x = -\frac{4}{3}
$$
$$
x - 6 = 0 \quad \Rightarrow \quad x = 6
$$

Thus, Elijah's first error was in Step 2, where he incorrectly grouped the terms.
Elijah made his first error in Step 2 by incorrectly grouping the terms.

a. Watch this video of Mrs. Hool completing a similar problem
b. Reattempt the question from your test:
i. Elijah is solving the quadratic equation by factoring.
His work is shown below. In which step did Elijah make his first error? What
is it?

Step 1:3x
Step 2:
Step 3:
Step
Step or
or

Upstudy AI Solution

Answer

Solution

Mind Expander

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a. Watch this video of Mrs. Hool completing a similar problem b. Reattempt the question from your test: i. Elijah is solving the quadratic equation by factoring. His work is shown below. In which step did Elijah make his first error? What is it? Step 1:3x Step 2: Step 3: Step Step or or

Upstudy AI Solution

Answer

Solution

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Latest Algebra Questions

a. Watch this video of Mrs. Hool completing a similar problem
b. Reattempt the question from your test:
i. Elijah is solving the quadratic equation by factoring.
His work is shown below. In which step did Elijah make his first error? What
is it?

Step 1:3x
Step 2:
Step 3:
Step
Step or
or