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

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

Answer 1

Let's analyze Jedida's work step by step:

1. Given Equation: \[ X^2 - 96 = 4X \]

2. Step 1: \[ X^2 - 96 - 4X = 0 \] Here, she should subtract \(4X\) from both sides, which she attempted but rewrote it incorrectly as \(X^3 + 4X - 96 = 0\). This is indeed a mistake, as there is no \(X^3\) involved in the equation.

3. Step 2: After making the error in Step 1, she proceeds to factor something that doesn't correctly represent the original equation. Since Step 1 was incorrect, any factoring that follows from that will also be incorrect.

4. Step 3: In this step, she applies the zero product property correctly given her factored form, but since her factoring in Step 2 was wrong, the solutions she arrives at are invalid, despite the process being correctly applied if the factorization were correct.

Thus, her first mistake occurred in Step 1 when she incorrectly added \(4X\) rather than subtracting it.

The correct answer is B. STEP 1; SHE ADDED 4 X TO BOTH SIDES INSTEAD OF SUBTRACTING.