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

To factor \(x^2 - x - 2\), find two numbers \(a\) and \(b\) such that \(a\times b=-2\) and \(a + b=-1\).

Step2: Identify numbers

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

Step3: Factor the quadratic

Rewrite the middle term: \(x^2-2x + x - 2\). Group: \((x^2-2x)+(x - 2)=x(x - 2)+1(x - 2)=(x - 2)(x + 1)\). Wait, but let's check the options. Wait, maybe miscalculation. Wait, let's expand each option:

• Option 1: \((x - 2)(x + 1)=x^2+x-2x - 2=x^2 - x - 2\) (correct). Wait, the marked option is \((x + 2)(x - 1)=x^2 - x+2x - 2=x^2+x - 2\) (wrong). Wait, maybe a mistake in the problem's marked option. But following factoring:

We need two numbers with product \(-2\) and sum \(-1\). The numbers are \(-2\) and \(1\). So factors are \((x - 2)(x + 1)\).

Answer:

A. \((x - 2)(x + 1)\)