QUADRATIC EQUATIONS UNIT TEST:

Question

JEDIDA SOLVED THE QUADRATIC EQUATION X 2 - 96 = 4X BY FACTORING. HER WORK IS SHOWN BELOW. AT WHICH STEP DID JEDIDA FIRST MAKE A MISTAKE, IF AT ALL?
X 2 - 96 = 4 X

STEP 1: X 3 + 4 X - 96 = 0 ADD 4X TO BOTH SIDES.
STEP 2: (X + 12) ( X - 8) = 0 FACTOR
SETP 3: X + 12 = 0 OR X - 8 = 0 USE THE ZERO PRODUCT PROPERTY.
X = -12 OR X = 8

STEP 2: SHE DID NOT FACTOR THE LEFT SIDE OF THE EQUATION CORRECTLY.
STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRAVTING.
SHE DID NOT MAKE ANY MISTAKES.
STEP 3; SHE DID NOT APPY THE ZERO PRODUCT PROPERTY CORRECTLY.

Answer 1

Let's review Jedida's work step by step to determine if she made any mistakes.

Starting with the original equation: \[ x^2 - 96 = 4x \]

To rearrange it, we need to move all terms to one side of the equation. We subtract \(4x\) from both sides: \[ x^2 - 4x - 96 = 0 \]

Now, looking at Jedida's Step 1: Jedida's Step 1: \( x^2 + 4x - 96 = 0 \) Here she added \(4x\) instead of subtracting it, which is incorrect. This is where her first mistake occurs.

Next: Jedida's Step 2: She factored incorrectly. The correct factorization of \(x^2 - 4x - 96\) should yield different factors. However, the error in Step 1 means that the factors she arrives at in Step 2 are already based on an incorrect equation.

Finally, Jedida's Step 3: While she uses the zero product property correctly to find the roots, her results are based on incorrect factors.

Based on this breakdown, the first mistake Jedida made was in Step 1 where she added \(4x\) to both sides instead of subtracting it. Therefore, the correct answer is:

STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRACTING.