Discussion
Which of the following are factors of \(x^{2} - x - 6\) ?
Answer: A
The factors are \((x + 2)\) and \((x - 3)\).
Find two numbers whose product is \(-6\) and whose sum is \(-1\): they are \(+2\) and \(-3\).
\[ x^{2} - x - 6 = (x + 2)(x - 3) \]
Check: \(x^{2} - 3x + 2x - 6 = x^{2} - x - 6\). The pair \((x - 2)(x + 3)\) gives \(x^{2} + x - 6\), with the wrong sign of the middle term, and \((x + 1)(x - 6)\) and \((x - 1)(x + 6)\) give middle terms of \(-5x\) and \(+5x\).
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