How do you factor the expression $x^2 - x -6$ ?

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Answer 1 · 2018-03-04T06:38:55

The factored expression $(x+2)(x-3)$ .

First, find two numbers that multiply to $-6$ (the $c$ value of the quadratic) and add up $-1$ (the $b$ value of the quadratic).

The two numbers are $-3$ and $2$ . Now, split $-x$ into $-3x$ and $2x$ . Then, group together the two factors:

$color(white)=x^2-x-6$

$=x^2-3x+2x-6$

$=color(red)x*x-color(red)x*3+2x-6$

$=color(red)x*x-color(red)x*3+color(blue)2*x-color(blue)2*3$

$=color(red)x(x-3)+color(blue)2*x-color(blue)2*3$

$=color(red)x(x-3)+color(blue)2(x-3)$

$=(color(red)x+color(blue)2)(x-3)$

That's the factored quadratic.

How do you factor the expression x^2 - x -6x^2 - x -6?