Removin common factor factoring?

Question

Removing a common factor inequalities?

say you have -x^2-x+6>0 you have to common factor - rite but since you divide everything in left side by -1 you have to divide everything on right side by negative one as well? so -(x^2+x-6)<0 and -(x-2)(x+3) <0 rite

Answer 1

You have just factored the left side,

you haven&#039;t divided it yet.

-x^2 - x +  6 &gt; 0

(-1)(x^2 + x - 6) &gt; 0

(-1) (x + 3) (x - 2) &gt; 0

Only if you remove the -1

do you have to change the &gt; to &lt;.

(x + 3) (x - 2) &lt; 0

Then x+3 and x-2 have opposite signs.

a) x + 3 &gt; 0 and x - 2 &lt; 0

x &gt; -3 and x &lt; 2

b) x + 3 &lt; 0 and x - 2 &gt; 0

x &lt; -3 and x &gt; 2

This case is impossible, as x cannot

simultaneously satisfy both of those.

So from case a we have

-3 &lt; x &lt; 2

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