Question

1. Kalena was asked to prove ifx(x - 1)(x + 1) = x3 - X represents a polynomial identity. She

states that this relationship is not true and the work she used to justify her thinking is shown.
Step 1: x(x - 1)(x + 1)
Step 2: (x2 + x)(x - 1)
Step 3: x3 - x2 - x2 - x
Step 4: x3 - 2x2 - x
Which statement correctly describes Kalena's justification?
A. Kalena is correct. There are no mistakes in her justification.
B. Kalena made a mistake in Step 2. The justification should state: (2x - x)(x + 1).
C. Kalena made a mistake in Step 3. The justification should state: x
- x.
D. Kalena made a mistake in Step 4. The justification should state: x3 + 2x2 - x

Answer 1

C. Kalena made a mistake in Step 3. The justification should state: -x²

+ x²

Explanation:

Given the function x(x - 1)(x + 1) = x3 - X

To justify kelena proof

We will need to show if the two equations are equal.

Starting from the RHS with function x³-x

First we will factor out the common factor which is 'x' to have;

x(x²-1)

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Note that for two real number a and b, the expansion of a²-b² using difference vof two square will give;

a²-b² = (a+b)(a-b) hence;

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Factorising x(x+1) gives x²+x, therefore

x(x+1)(x-1) = (x²+x)(x-1)

(x²+x)(x-1) = x³-x²+x²-x

The function x³-x²+x²-x gotten shows that kelena made a mistake in step 3, the justification should be -x²+x² not -x-x²