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the equation: x3 - 6x2 + 11x -6
Becasuse it intersects at the x axis, y=0 so we set the equation equal to 0. x3 - 6x2 + 11x -6 =0
we know it intersects the x axis at 1 and so (x-1) is a factor of that equation. so it becomes (x-1)*(Ax2 +Bx +C) where A,B,C are intergers to be found.
we divide (x-1) from the orginal equation x3 - 6x2 + 11x -6.
x3 - 6x2 + 11x -6/(x-1) = x2-5x+6
This means we can write the orignal equation x3 - 6x2 + 11x -6 = (x-1)*(x2-5x+6)
we factorise the quadractic equation x2-5x+6. This will become (x-2)(x-3)
Therefore X=2 and X=3, therfore the other two points of intersection are 2 and 3.see more