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

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Answer 1 · 2015-06-04T20:40:38

Notice that $3 \times 2 = 6$ $3xx2 = 6$ and $3 - 2 = 1$ $3-2=1$ .

So

$(x + 3) (x - 2) = x^{2} + 3 x - 2 x - (3 \times 2)$ $(x+3)(x-2) = x^2+3x-2x-(3xx2)$

$= x^{2} + (3 - 2) x - (3 \times 2) = x^{2} + x - 6$ $= x^2+(3-2)x-(3xx2) = x^2+x-6$

This is an instance of the general form:

$(x + a) (x - b) = x^{2} + (a - b) x - a b$ $(x+a)(x-b) = x^2+(a-b)x-ab$

How do you factor x2+x−6x^2 + x - 6?