Question 7 (2 points) Factor completely: x^2-x-6 (x+1)(x-6) b (x+2)(x-3) c (x-2)(x+3) d (x-1)(x+6)

To factor the quadratic expression \(x^2 - x - 6\) completely, we need to find two numbers that multiply to \(-6\) (the constant term) and add up to \(-1\) (the coefficient of the linear term).<br /><br />Let's find these two numbers:<br /><br />1. The product of the two numbers should be \(-6\).<br />2. The sum of the two numbers should be \(-1\).<br /><br />The two numbers that satisfy these conditions are \(-3\) and \(2\), because:<br />- \((-3) \times 2 = -6\)<br />- \((-3) + 2 = -1\)<br /><br />Therefore, we can write the quadratic expression as:<br />\[ x^2 - x - 6 = (x - 3)(x + 2) \]<br /><br />So, the correct answer is:<br />b) \((x+2)(x-3)\)