(1) FactorizeOriginally Posted byBrian D

x^2 - 4x + 3 = (x-3)*(x-1)

(2) Think, when is (x-3)*(x-1) negative (less than zero)? When each parenthetical group has a different sign.

Possibilities:

(a) x<3 making (x-3) negative AND x>1 making (x-1) positive

(b) x>3 making (x-3) positive AND x<1 making (x-1) negative

Therefore, 1<x<3

On a number line, open circles at 1 and 3 and connect them.