Question

what is the factored form of ( x^2 - x - 2 )?
\\( (x - 2)(x + 1) \\)
\\( (x + 2)(x + 1) \\)
\\( (x - 2)(x - 1) \\)
\\( (x + 2)(x - 1) \\)

Explanation:

Step1: Recall factoring quadratic

We need to factor \(x^2 - x - 2\). Find two numbers that multiply to \(-2\) and add to \(-1\).

Step2: Identify the numbers

The numbers are \(-2\) and \(1\) (since \(-2\times1 = -2\) and \(-2 + 1=-1\)).

Step3: Write the factored form

So, \(x^2 - x - 2=(x - 2)(x + 1)\)? Wait, no, wait: let's expand \((x + 2)(x - 1)\): \(x^2 - x + 2x - 2=x^2 + x - 2\). No. Wait, \((x - 2)(x + 1)=x^2 + x - 2x - 2=x^2 - x - 2\). Wait, no, wait: \((x - 2)(x + 1)=x^2 + x - 2x - 2=x^2 - x - 2\). Wait, but let's check the options. Wait, the options are:

1. \((x - 2)(x + 1)\)
2. \((x + 2)(x + 1)\)
3. \((x - 2)(x - 1)\)
4. \((x + 2)(x - 1)\)

Let's expand each:

• Option 1: \((x - 2)(x + 1)=x^2 + x - 2x - 2=x^2 - x - 2\) (matches)
• Option 2: \((x + 2)(x + 1)=x^2 + x + 2x + 2=x^2 + 3x + 2\) (no)
• Option 3: \((x - 2)(x - 1)=x^2 - x - 2x + 2=x^2 - 3x + 2\) (no)
• Option 4: \((x + 2)(x - 1)=x^2 - x + 2x - 2=x^2 + x - 2\) (no)

Wait, so the correct factoring is \((x - 2)(x + 1)\), which is the first option.

Answer:

\((x - 2)(x + 1)\) (the first option)