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

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Answer 1 · 2018-03-04T06:38:55

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

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

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

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

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

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

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

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

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

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

That's the factored quadratic.

How do you factor the expression x2−x−6x^2 - x -6?