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.

Question

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 .

Answer 1

Karim's first mistake occurs at Step 1.

The original quadratic equation is \( x^2 + 5x - 24 = 0 \). When he attempts to rewrite the middle term \( 5x \), he incorrectly writes it as \( 8x + (-3x) \).

The correct way to split the term \( 5x \) for factoring would be to express it as \( 8x - 3x \) or another valid pair of factors that add up to \( 5x \).

Thus, the correct first step should have been \( x^2 + 8x - 3x - 24 = 0 \) (which also isn't valid after checking) or finding two numbers that multiply to \( -24 \) and add up to \( 5 \) (which would be \( 8 \) and \( -3 \)).

The correct grouping would have been splitting \( 5x \) as \( 8x - 3x \) and not \( 8x + (-3x) \).