Question

Karim is solving the quadratic equation x2+5x−24=0
by grouping. His work is shown below. Determine the first step at which Karim makes an error.

Step 1: x2+8x+(−3x)−24=0

Step 2: (x2+8x)+(−3x−24)=0

Step 3: x(x+8)+3(x+8)=0

Step 4: (x+8)(x+3)=0

Step 5: x+8=0
or x+3=0

x=−8
or x=−3

(1 point)
Karim's first mistake occurs at Step
.
Remaining Attempts : 3
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Answer 1

To determine the first step at which Karim makes an error, let's examine each step carefully.

**Step 1:** \( x^2 + 8x + (-3x) - 24 = 0 \)
Here, Karim attempts to factor the quadratic expression, but \( 8x \) is incorrect. To correctly group the middle term, it should be split into two terms that add to \( 5x \) (the coefficient of x in \( x^2 + 5x - 24 \)).

**Step 2:** \( (x^2 + 8x) + (-3x - 24) = 0 \)
This step is based on the incorrect first step and continues the error.

**Step 3:** \( x(x + 8) + 3(x + 8) = 0 \)
This step assumes the grouping was correct, but since Step 1 was already incorrect, this is also wrong.

**Step 4:** \( (x + 8)(x + 3) = 0 \)
This factorization is based on the flawed previous steps.

**Step 5:** Solving gives \( x + 8 = 0 \) or \( x + 3 = 0 \), correctly yielding \( x = -8 \) or \( x = -3 \).

The first step at which Karim makes an error is **Step 1**, where he incorrectly splits \( 5x \) into \( 8x \) and \( -3x \).

**Final Answer:** Step 1.